From 623c52c706b5b6eae8f04ce015d50e8bf713ed9a Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 4 Sep 2024 03:15:13 +0000 Subject: [PATCH] build based on 8f60515 --- stable | 2 +- v1 | 2 +- v1.1 | 2 +- v1.1.5/.documenter-siteinfo.json | 1 + v1.1.5/MeshData/index.html | 32 + v1.1.5/RefElemData/index.html | 46 + v1.1.5/assets/documenter.js | 1064 +++++++++++++++++ v1.1.5/assets/dudx.png | Bin 0 -> 87439 bytes v1.1.5/assets/hicken_N4.png | Bin 0 -> 14420 bytes v1.1.5/assets/hohqmesh.png | Bin 0 -> 32970 bytes v1.1.5/assets/kubatko_legendre_N4.png | Bin 0 -> 12398 bytes v1.1.5/assets/kubatko_lobatto_N4.png | Bin 0 -> 13235 bytes v1.1.5/assets/mapping_diagram.png | Bin 0 -> 489244 bytes v1.1.5/assets/scramjet.png | Bin 0 -> 461851 bytes v1.1.5/assets/test_ck45.jl | 29 + v1.1.5/assets/themes/catppuccin-frappe.css | 1 + v1.1.5/assets/themes/catppuccin-latte.css | 1 + v1.1.5/assets/themes/catppuccin-macchiato.css | 1 + v1.1.5/assets/themes/catppuccin-mocha.css | 1 + v1.1.5/assets/themes/documenter-dark.css | 7 + v1.1.5/assets/themes/documenter-light.css | 9 + v1.1.5/assets/themeswap.js | 84 ++ v1.1.5/assets/u.png | Bin 0 -> 85926 bytes v1.1.5/assets/warner.js | 52 + v1.1.5/conventions/index.html | 2 + v1.1.5/ex_dg_deriv/index.html | 28 + v1.1.5/index.html | 20 + v1.1.5/index_refs/index.html | 105 ++ v1.1.5/more_meshes/index.html | 52 + v1.1.5/objects.inv | Bin 0 -> 2816 bytes v1.1.5/search_index.js | 3 + v1.1.5/siteinfo.js | 1 + v1.1.5/tstep_usage/index.html | 30 + versions.js | 2 +- 34 files changed, 1573 insertions(+), 4 deletions(-) create mode 100644 v1.1.5/.documenter-siteinfo.json create mode 100644 v1.1.5/MeshData/index.html create mode 100644 v1.1.5/RefElemData/index.html create mode 100644 v1.1.5/assets/documenter.js create mode 100644 v1.1.5/assets/dudx.png create mode 100644 v1.1.5/assets/hicken_N4.png create mode 100644 v1.1.5/assets/hohqmesh.png create mode 100644 v1.1.5/assets/kubatko_legendre_N4.png create mode 100644 v1.1.5/assets/kubatko_lobatto_N4.png create mode 100644 v1.1.5/assets/mapping_diagram.png create mode 100644 v1.1.5/assets/scramjet.png create mode 100644 v1.1.5/assets/test_ck45.jl create mode 100644 v1.1.5/assets/themes/catppuccin-frappe.css create mode 100644 v1.1.5/assets/themes/catppuccin-latte.css create mode 100644 v1.1.5/assets/themes/catppuccin-macchiato.css create mode 100644 v1.1.5/assets/themes/catppuccin-mocha.css create mode 100644 v1.1.5/assets/themes/documenter-dark.css create mode 100644 v1.1.5/assets/themes/documenter-light.css create mode 100644 v1.1.5/assets/themeswap.js create mode 100644 v1.1.5/assets/u.png create mode 100644 v1.1.5/assets/warner.js create mode 100644 v1.1.5/conventions/index.html create mode 100644 v1.1.5/ex_dg_deriv/index.html create mode 100644 v1.1.5/index.html create mode 100644 v1.1.5/index_refs/index.html create mode 100644 v1.1.5/more_meshes/index.html create mode 100644 v1.1.5/objects.inv create mode 100644 v1.1.5/search_index.js create mode 100644 v1.1.5/siteinfo.js create mode 100644 v1.1.5/tstep_usage/index.html diff --git a/stable b/stable index 89fb16f8..261f3475 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v1.1.4 \ No newline at end of file +v1.1.5 \ No newline at end of file diff --git a/v1 b/v1 index 89fb16f8..261f3475 120000 --- a/v1 +++ b/v1 @@ -1 +1 @@ -v1.1.4 \ No newline at end of file +v1.1.5 \ No newline at end of file diff --git a/v1.1 b/v1.1 index 89fb16f8..261f3475 120000 --- a/v1.1 +++ b/v1.1 @@ -1 +1 @@ -v1.1.4 \ No newline at end of file +v1.1.5 \ No newline at end of file diff --git a/v1.1.5/.documenter-siteinfo.json b/v1.1.5/.documenter-siteinfo.json new file mode 100644 index 00000000..6cfc4f1b --- /dev/null +++ b/v1.1.5/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-04T03:15:08","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/v1.1.5/MeshData/index.html b/v1.1.5/MeshData/index.html new file mode 100644 index 00000000..efd1f1c7 --- /dev/null +++ b/v1.1.5/MeshData/index.html @@ -0,0 +1,32 @@ + +MeshData · StartUpDG.jl

MeshData type

MeshData includes fields such as

  • xyz::NTuple{Dim, ...}: nodal interpolation points mapped to physical elements. All elements of xyz are $N_p \times N_{\rm elements}$ matrices, where $N_p$ are the number of nodal points on each element.
  • xyzq::NTuple{Dim, ...}, wJq: volume quadrature points/weights mapped to physical elements. All elements these tuples are $N_q \times N_{\rm elements}$ matrices, where $N_q$ is the number of quadrature points on each element.
  • xyzf::NTuple{Dim, ...}: face quadrature points mapped to physical elements. All elements of xyz are $N_f \times N_{\rm elements}$ matrices, where $N_f$ is the number of face points on each element.
  • mapP, mapB: indexing arrays for inter-element node connectivity (mapP) and for extracting boundary nodes from the list of face nodes xyzf (mapB). mapP is a matrix of size $N_f \times N_{\rm elements}$, while the length of mapB is the total number of nodes on the boundary.
  • rstxyzJ::SMatrix{Dim, Dim}: volume geometric terms $G_{ij} = \frac{\partial x_i}{\partial \hat{x}_j}$. Each element of rstxyzJ is a matrix of size $N_p \times N_{\rm elements}$.
  • J, Jf: volume and surface Jacobians evaluated at interpolation points and surface quadrature points, respectively. J is a matrix of size $N_p \times N_{\rm elements}$, while Jf is a matrix of size $N_f \times N_{\rm elements}$.
  • nxyz::NTuple{Dim, ...} and nxyzJ::NTuple{Dim, ...}: normalized and Jf scaled outward normals evaluated at surface quadrature points. Each element of nxyzJ is a matrix of size $N_f \times N_{\rm elements}$.

These are the main quantities used to construct a DG solver. Information specific to the type of mesh used is stored in the md.mesh_type field.

Setting up md::MeshData

The MeshData struct contains data for high order DG methods useful for evaluating DG formulations in a matrix-free fashion.

Generating unstructured meshes

For convenience, simple uniform meshes are included in with StartUpDG.jl via uniform_mesh

using StartUpDG
+num_cells_x, num_cells_y, num_cells_z = 4, 2, 8
+(VX,), EToV = uniform_mesh(Line(), num_cells_x)
+(VX, VY), EToV = uniform_mesh(Tri(), num_cells_x, num_cells_y)
+(VX, VY), EToV = uniform_mesh(Quad(), num_cells_x, num_cells_y)
+(VX, VY, VZ), EToV = uniform_mesh(Tet(), num_cells_x, num_cells_y, num_cells_z)
+(VX, VY, VZ), EToV = uniform_mesh(Pyr(), num_cells_x, num_cells_y, num_cells_z)
+(VX, VY, VZ), EToV = uniform_mesh(Wedge(), num_cells_x, num_cells_y, num_cells_z)
+(VX, VY, VZ), EToV = uniform_mesh(Hex(), num_cells_x, num_cells_y, num_cells_z)

The uniform triangular mesh is constructed by creating a uniform quadrilateral mesh then bisecting each quad into two triangles. Wedge meshes are constructed similarly. Tet meshes are constructed by dividing each hexahedron into 5 tetrahedral elements. Pyramid meshes are constructed by dividing each hexahedron into 6 pyramids.

Initializing high order DG mesh data

Given unstructured mesh information (tuple of vertex coordinates VXYZ and index array EToV) high order DG mesh data can be constructed as follows:

md = MeshData(VXYZ, EToV, rd)

Enforcing periodic boundary conditions

Periodic boundary conditions can be enforced via the is_periodic keyword argument 

md_periodic = MeshData((VX, VY), EToV, rd; is_periodic=true) # periodic in both x and y coordinates
+md_periodic_x = MeshData((VX, VY), EToV, rd; is_periodic=(true, false)) # periodic in x direction, but not y

or by calling make_periodic, which returns a new MeshData instance

md = MeshData((VX, VY), EToV, rd)
+md_periodic = make_periodic(md) # periodic in both x and y coordinates
+md_periodic_x = make_periodic(md, true, false) # periodic in x direction, but not y

In either case, the MeshData indexing arrays fields mapP,mapB, and FToF are modified to account for periodicity.

One can check which dimensions are periodic via the is_periodic field of MeshData. For example, the md_periodic_x example above gives

julia> md_periodic_x.is_periodic
+(true, false)

Creating curved meshes

It is common to generate curved meshes by first generating a linear mesh, then moving high order nodes on the linear mesh. This can be done by calling MeshData again with new x, y coordinates:

md = MeshData((VX, VY), EToV, rd)
+(; x, y ) = md
+# <-- code to modify high order nodes (x,y)
+md_curved = MeshData(rd, md, x, y)

MeshData(rd, md, x, y) and MeshData(rd, md, x, y, z) are implemented for 2D and 3D, though this is not currently implemented in 1D.

More generally, one can create a copy of a MeshData with certain fields modified by using @set or setproperties from Setfield.jl.

Unstructured and pre-defined triangular meshes using Triangulate.jl

StartUpDG.jl also includes additional utilities based on Triangulate.jl for creating and visualizing meshes. Several pre-defined geometries are included in StartUpDG.jl. A few examples are SquareDomain, RectangularDomainWithHole, Scramjet, and CircularDomain. See triangulate_example_meshes.jl for a more complete list and field arguments. These can each be called using triangulate_domain, for example the following code will create a mesh of a scramjet:

meshIO = triangulate_domain(Scramjet())
+(VX, VY), EToV = triangulateIO_to_VXYEToV(meshIO)
+rd = RefElemData(Tri(), 7)
+md = MeshData((VX, VY), EToV, rd)

A quick plot of the face nodes via 

using Plots
+scatter(vec.(md.xyzf)..., msw=0, ms=1, aspect_ratio=:equal, ylims=(0,2), leg=false)

shows the following figure u

Unstructured curved quadrilateral and hexahedral meshes using HOHQMesh.jl

StartUpDG.jl also reads in .mesh files generated by HOHQMesh.jl. The following code constructs a MeshData which represents a curved quadrilateral mesh generated by HOHQMesh.jl. 

using StartUpDG
+rd = RefElemData(Quad(), 4)
+hmd = read_HOHQMesh("test/testset_HOHQMesh_meshes/easy_example.mesh", Quad())
+md = MeshData(hmd, rd)

We can visualize the mesh using 

using Plots
+plot(rd, md) # can also use `plot(MeshPlotter(rd, md))`

which yields the following figure:

u

The boundary faces are also automatically tagged with the labels provided in the HOHQMesh file. Each boundary tag and the faces that lie on it are stored in md.mesh_type.boundary_faces.

Tagging boundary faces and boundary nodes

One can "tag" boundary faces (or boundary nodes) by specifying boolean functions which evaluate to true if a point is on a given boundary segment. 

rd = RefElemData(Tri(), N=3)
+md = MeshData(uniform_mesh(Tri(), 1)..., rd)
+on_bottom_boundary(point, tol=1e-13) = abs(point[2] + 1) < tol # point = (x,y)
+on_top_boundary(point, tol=1e-13) = abs(point[2] - 1) < tol    
+
+boundary_face_dict = tag_boundary_faces(md, Dict(:bottom => on_bottom_boundary, :top => on_top_boundary))
+boundary_node_dict = tag_boundary_nodes(rd, md, Dict(:bottom => on_bottom_boundary, :top => on_top_boundary))

You can also specify a list of boundaries using NamedTuples 

boundary_face_dict = tag_boundary_faces(md, (; :bottom=>on_bottom_boundary,:top=>on_top_boundary))
+boundary_node_dict = tag_boundary_nodes(rd, md, (; :bottom=>on_bottom_boundary,:top=>on_top_boundary))
diff --git a/v1.1.5/RefElemData/index.html b/v1.1.5/RefElemData/index.html new file mode 100644 index 00000000..14faf1a9 --- /dev/null +++ b/v1.1.5/RefElemData/index.html @@ -0,0 +1,46 @@ + +RefElemData · StartUpDG.jl

RefElemData type

RefElemData contains the following fields

  • element_type::AbstractElemShape: element shape. Line, Tri, Quad, Hex, Wedge, Pyr, Tet currently supported.
  • approximation_type: approximation type. Defaults to Polynomial(), but SBP() is also supported (see RefElemData based on SBP finite differences).
  • Nfaces: number of faces on a given type of reference element.
  • fv: list of vertices defining faces, e.g., [1,2], [2,3], [3,1] for a triangle
  • Fmask: indices of interpolation nodes which lie on the faces
  • VDM: the generalized Vandermonde matrix, a square matrix whose columns are $V_{ij} = \phi_{j}(x_i}$, where $\phi_j$ are orthonormal basis functions and $x_i$ are interpolation points.
  • rst::NTuple{Dim, ...}: tuple of vectors of length N_p, each of which contains coordinates of degree $N$ optimized polynomial interpolation points.
  • rstq::NTuple{Dim, ...},wq, Vq: tuple of volume quadrature points, vector of weights, and quadrature interpolation matrix. Each element of rstq and wq are vectors of length $N_q$, and Vq is a matrix of size $N_q \times N_p$.
  • N_{\rm plot}: the degree which determines the number of plotting points $N_{p,{\rm plot}}$.
  • rstp::NTuple{Dim, ...}, Vp: tuple of plotting points and plotting interpolation matrix. Each element of rstp is a vector of length $N_{p,{\rm plot}}$, and Vp is a matrix of size $N_{p,{\rm plot}} \times N_p$.
  • rstf::NTuple{Dim, ...},wf, Vf: tuple of face quadrature points, weights, and face interpolation matrix. Each element of rstf and wf are vectors of length $N_f$, and Vf is a matrix of size $N_f \times N_p$.
  • nrstJ::NTuple{Dim, ...}: tuple of outward reference normals, scaled by the face Jacobian. Each element is a vector of length $N_f$.
  • M: mass matrix computed using quadrature. Size $N_p \times N_p$
  • Pq: quadrature-based $L^2$ projection matrix. Size $N_p \times N_q$.
  • Drst::NTuple{Dim, ...}, LIFT: differentiation and lifting matrices. Differentiation matrices are size $N_p \times N_p,$ while lift matrices are size $N_p\times N_f$.

This list is incomplete; other fields are stored or accessible but currently only used for internal computations.

Mass, differentiation, lifting, and interpolation matrices can be specialized. For example, these matrices are dense Matrix{T} type for lines and triangles, but could also be stored as sparse matrices for quadrilaterals and hexahedra.

Setting up rd::RefElemData

The struct rd::RefElemData contains data for a given element type. All common reference elements are supported: Line, Tri, Quad, Tet, Pyr, Wedge, and Hex.

To initalize a RefElemData, just specify the element type and polynomial degree.

N = 3
+
+# 1D elements 
+rd = RefElemData(Line(), N)
+
+# 2D elements
+rd = RefElemData(Tri(), N)
+rd = RefElemData(Quad(), N)
+
+# 3D elements
+rd = RefElemData(Tet(), N)
+rd = RefElemData(Pyr(), N)
+rd = RefElemData(Wedge(), N)
+rd = RefElemData(Hex(), N)

Specifying different quadrature rules.

By default, RefElemData initializes volume and surface quadrature rules to be the minimum rules which exactly integrate the unweighted volume and surface mass matrices. If different quadrature rules are desired, they can be specified as follows: 

N = 3
+
+# create degree N tensor product Gauss-Lobatto rule
+r1D, w1D = gauss_lobatto_quad(0, 0, N)
+rq, sq = vec.(StartUpDG.meshgrid(r1D))
+wr, ws = vec.(StartUpDG.meshgrid(w1D))
+wq = @. wr * ws
+
+rd = RefElemData(Quad(), N; quad_rule_vol = (rq, sq, wq),  
+                           quad_rule_face = (r1D, w1D))

This results in a DG spectral element method (DG-SEM) discretization, with a diagonal lumped mass matrix and differentiation matrices which satisfy a summation-by-parts property.

By default, RefElemData is constructed for a nodal basis (in order to facilitate curved meshes, connectivity, etc). The interpolation nodes are computed using an interpolatory version of the warp-and-blend procedure.

Note

While specifying the quadrature rule changes the discretization, it is not reflected in the RefElemData type and thus cannot be specialized on. The following constructors produce RefElemData where the quadrature structure is reflected in the type parameters:

rd = RefElemData(Hex(), Polynomial(TensorProductQuadrature(quad_nodes(Line(), N+1)), N)) # tensor product quadrature rules
+rd = RefElemData(Quad(), Polynomial{Gauss}(), N) # (N+1)^d point tensor product Gauss quadrature

RefElemData based on SBP finite differences

It is also possible to construct a RefElemData based on both traditional finite difference SBP operators and multi-dimensional SBP finite difference operators. The traditional finite difference SBP operators are built using SummationByPartsOperators.jl. The multi-dimensional SBP operators utilize nodes constructed by Tianheng Chen and Chi-Wang Shu, Ethan Kubatko, and Jason Hicken.

Some examples of traditional finite difference SBP operators on tensor product domains:

using StartUpDG
+using SummationByPartsOperators # this package must be loaded to enable extension
+
+D = derivative_operator(MattssonNordström2004(), 
+                        derivative_order=1, accuracy_order=N+1,
+                        xmin=-1.0, xmax=1.0, N=20)
+
+rd = RefElemData(Line(), D) 
+rd = RefElemData(Quad(), D)
+rd = RefElemData(Hex(), D)

Some examples of multi-dimensional SBP operators:

N = 3
+rd = RefElemData(Quad(), SBP(), N) # defaults to SBP{TensorProductLobatto}
+rd = RefElemData(Quad(), SBP{TensorProductLobatto}(), N) 
+
+rd = RefElemData(Hex(), SBP(), N) # defaults to SBP{TensorProductLobatto}
+rd = RefElemData(Hex(), SBP{TensorProductLobatto}(), N) 
+
+rd = RefElemData(Tri(),  SBP(), N) # defaults to SBP{Kubatko{LobattoFaceNodes}}
+rd = RefElemData(Tri(),  SBP{Hicken}(), N) 
+rd = RefElemData(Tri(),  SBP{Kubatko{LobattoFaceNodes}}(), N) 
+rd = RefElemData(Tri(),  SBP{Kubatko{LegendreFaceNodes}}(), N)

Quadrature rules of both degree 2*N-1 (up to N = 6) and 2*N (up to N = 4) are supported on triangles. For Line, Quad, and Hex elements, RefElemData(..., SBP(), N) is the same as the RefElemData for a DG-SEM discretization, though some fields are specialized for the SBP type. These SBP-based RefElemData objects can also be used to initialize a mesh (for example, md = MeshData(uniform_mesh(rd.element_type, 4)..., rd)).

On triangles, we have the following SBP types with the following properties:

  • SBP{Kubatko{LobattoFaceNodes}}: degree 2N-1 accurate quadrature rules with N+2 Lobatto nodes on each face. Nodes for N=4:

klobatto4

  • SBP{Kubatko{LegendreFaceNodes}}: degree 2N-1 accurate quadrature rules with N+1 Legendre nodes on each face. For N = 1,...,4, these are the same as the nodes constructed by Chen and Shu. Nodes for N=4:

klegendre4

  • SBP{Hicken}: degree 2N accurate quadrature rules with N+2 Lobatto nodes on each face. Nodes for N=4:

hicken4

Tensor product RefElemData on wedge elements

Experimental implementation

This is an experimental feature and may change in future releases.

There is experimental support for RefElemDatas created from tensor products of triangular and 1D RefElemData objects. 

line = RefElemData(Line(), N_line)
+tri  = RefElemData(Tri(), N_tri)
+rd   = RefElemData(Wedge(), TensorProductWedge(tri, line))

This new rd::RefElemData can then be used to create a wedge-based MeshData. The individual RefElemData objects can be accessed from rd.approximation_type::TensorProductWedge.

diff --git a/v1.1.5/assets/documenter.js b/v1.1.5/assets/documenter.js new file mode 100644 index 00000000..82252a11 --- /dev/null +++ b/v1.1.5/assets/documenter.js @@ -0,0 +1,1064 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v1.1.5/assets/dudx.png b/v1.1.5/assets/dudx.png new file mode 100644 index 0000000000000000000000000000000000000000..4007ec6af9607e6da2369876304a546003f6421b GIT binary patch literal 87439 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    uv5lD$-Nm|I4DYZ|TD+r{k{#uSoGIO}o80FKd~vq+1L$%4(RFu72&s_2YMf zv!sWqMdW|^H}CiQL!2_*;pXGF%NMNnzBT{%c5n**W5SZvAhbN_=F=B1Z*loY|6UFp z2hoCzgUp%{J(=;s;})scX>WF?TsiJpqQk4@TBiqYeu3QxDX!3&7n~iA2l4a$2Mx4g zR{<53aB(<(Nx^8;MC_q78jje*Wi<7S<{4Zi%V?e%%`+JF(}3195B@Wnb9}m6`&NvH P0SG)@{an^LB{Ts5@Evtd literal 0 HcmV?d00001 diff --git a/v1.1.5/assets/test_ck45.jl b/v1.1.5/assets/test_ck45.jl new file mode 100644 index 00000000..3fa771d2 --- /dev/null +++ b/v1.1.5/assets/test_ck45.jl @@ -0,0 +1,29 @@ +using Plots +using StartUpDG + +# Brusselator +B = 3 +f(y1,y2) = [1+y1^2*y2-(B+1)*y1, B*y1-y1^2*y2] +f(Q) = f(Q[1],Q[2]) +p,q = 1.5, 3.0 +Q = [p;q] + +dt = .1 +FinalTime = 20 + +res = zero.(Q) # init RK residual +rk4a,rk4b,rk4c = ck45() +Nsteps = ceil(FinalTime/dt) +dt = FinalTime/Nsteps + +plot() # init plot +for i = 1:Nsteps + global res # yes, I know...this is just for simplicty + for INTRK=1:5 + rhsQ = f(Q) + @. res = rk4a[INTRK]*res + dt*rhsQ # i = RK stage + @. Q = Q + rk4b[INTRK]*res + end + scatter!([i*dt;i*dt],Q) +end +display(plot!(leg=false)) diff --git a/v1.1.5/assets/themes/catppuccin-frappe.css b/v1.1.5/assets/themes/catppuccin-frappe.css new file mode 100644 index 00000000..32e3f008 --- /dev/null +++ b/v1.1.5/assets/themes/catppuccin-frappe.css @@ -0,0 +1 @@ +html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis,html.theme--catppuccin-frappe .file-cta,html.theme--catppuccin-frappe .file-name,html.theme--catppuccin-frappe .select select,html.theme--catppuccin-frappe .textarea,html.theme--catppuccin-frappe .input,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-frappe .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-frappe .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-primary.is-light,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:hover,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-frappe .button.is-primary.is-light.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-light.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:hover,html.theme--catppuccin-frappe .button.is-link.is-hovered{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus,html.theme--catppuccin-frappe 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-light{background-color:#edf2fc;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:hover,html.theme--catppuccin-frappe .button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:hover,html.theme--catppuccin-frappe .button.is-success.is-hovered{background-color:#9fcd80;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus,html.theme--catppuccin-frappe .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success:focus:not(:active),html.theme--catppuccin-frappe .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,209,137,0.25)}html.theme--catppuccin-frappe .button.is-success:active,html.theme--catppuccin-frappe .button.is-success.is-active{background-color:#98ca77;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe 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.button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter 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select:not([multiple]){padding-right:2.5em}html.theme--catppuccin-frappe .select select[multiple]{height:auto;padding:0}html.theme--catppuccin-frappe .select select[multiple] option{padding:0.5em 1em}html.theme--catppuccin-frappe .select:not(.is-multiple):not(.is-loading):hover::after{border-color:#99d1db}html.theme--catppuccin-frappe .select.is-white:not(:hover)::after{border-color:#fff}html.theme--catppuccin-frappe .select.is-white select{border-color:#fff}html.theme--catppuccin-frappe .select.is-white select:hover,html.theme--catppuccin-frappe .select.is-white select.is-hovered{border-color:#f2f2f2}html.theme--catppuccin-frappe .select.is-white select:focus,html.theme--catppuccin-frappe .select.is-white select.is-focused,html.theme--catppuccin-frappe .select.is-white select:active,html.theme--catppuccin-frappe .select.is-white select.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-frappe 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select.is-focused,html.theme--catppuccin-frappe .select.is-dark select:active,html.theme--catppuccin-frappe .content kbd.select select:active,html.theme--catppuccin-frappe .select.is-dark select.is-active,html.theme--catppuccin-frappe .content kbd.select select.is-active{box-shadow:0 0 0 0.125em rgba(65,69,89,0.25)}html.theme--catppuccin-frappe .select.is-primary:not(:hover)::after,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink:not(:hover)::after{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-primary select,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-primary select:hover,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:hover,html.theme--catppuccin-frappe .select.is-primary select.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-hovered{border-color:#769aeb}html.theme--catppuccin-frappe .select.is-primary select:focus,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:focus,html.theme--catppuccin-frappe .select.is-primary select.is-focused,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-focused,html.theme--catppuccin-frappe .select.is-primary select:active,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select:active,html.theme--catppuccin-frappe .select.is-primary select.is-active,html.theme--catppuccin-frappe .docstring>section>a.select.docs-sourcelink select.is-active{box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .select.is-link:not(:hover)::after{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-link select{border-color:#8caaee}html.theme--catppuccin-frappe .select.is-link select:hover,html.theme--catppuccin-frappe .select.is-link select.is-hovered{border-color:#769aeb}html.theme--catppuccin-frappe .select.is-link select:focus,html.theme--catppuccin-frappe .select.is-link select.is-focused,html.theme--catppuccin-frappe .select.is-link select:active,html.theme--catppuccin-frappe .select.is-link select.is-active{box-shadow:0 0 0 0.125em rgba(140,170,238,0.25)}html.theme--catppuccin-frappe .select.is-info:not(:hover)::after{border-color:#81c8be}html.theme--catppuccin-frappe .select.is-info select{border-color:#81c8be}html.theme--catppuccin-frappe .select.is-info select:hover,html.theme--catppuccin-frappe .select.is-info select.is-hovered{border-color:#6fc0b5}html.theme--catppuccin-frappe .select.is-info select:focus,html.theme--catppuccin-frappe .select.is-info select.is-focused,html.theme--catppuccin-frappe .select.is-info select:active,html.theme--catppuccin-frappe .select.is-info select.is-active{box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe 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a.navbar-item:focus,html.theme--catppuccin-frappe a.navbar-item:focus-within,html.theme--catppuccin-frappe a.navbar-item:hover,html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link:focus,html.theme--catppuccin-frappe .navbar-link:focus-within,html.theme--catppuccin-frappe .navbar-link:hover,html.theme--catppuccin-frappe .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#8caaee}html.theme--catppuccin-frappe .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .navbar-item img{max-height:1.75rem}html.theme--catppuccin-frappe .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-frappe .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-frappe .navbar-item.is-tab:focus,html.theme--catppuccin-frappe .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee}html.theme--catppuccin-frappe .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee;border-bottom-style:solid;border-bottom-width:3px;color:#8caaee;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-frappe .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-frappe .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-frappe .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-frappe .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-frappe 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#838ba7}html.theme--catppuccin-frappe .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#8caaee}.navbar.is-spaced html.theme--catppuccin-frappe .navbar-dropdown,html.theme--catppuccin-frappe .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-frappe .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-frappe .navbar-divider{display:block}html.theme--catppuccin-frappe .navbar>.container .navbar-brand,html.theme--catppuccin-frappe .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-frappe .navbar>.container .navbar-menu,html.theme--catppuccin-frappe .container>.navbar 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-previous,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-frappe .pagination.is-rounded .pagination-next,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-link,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-frappe .pagination,html.theme--catppuccin-frappe .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link{border-color:#626880;color:#8caaee;min-width:2.5em}html.theme--catppuccin-frappe .pagination-previous:hover,html.theme--catppuccin-frappe .pagination-next:hover,html.theme--catppuccin-frappe .pagination-link:hover{border-color:#737994;color:#99d1db}html.theme--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe .pagination-link:focus{border-color:#737994}html.theme--catppuccin-frappe .pagination-previous:active,html.theme--catppuccin-frappe .pagination-next:active,html.theme--catppuccin-frappe .pagination-link:active{box-shadow:inset 0 1px 2px 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768px){html.theme--catppuccin-frappe .pagination{flex-wrap:wrap}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-frappe .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination-previous{order:2}html.theme--catppuccin-frappe .pagination-next{order:3}html.theme--catppuccin-frappe .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-frappe .pagination.is-centered 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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table 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#documenter .docs-sidebar form.docs-search>input.file{font-size:.75rem}html.theme--catppuccin-latte .file.is-normal{font-size:1rem}html.theme--catppuccin-latte .file.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .file.is-medium .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-large{font-size:1.5rem}html.theme--catppuccin-latte .file.is-large .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.has-name .file-cta{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .file.has-name .file-name{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .file.has-name.is-empty .file-cta{border-radius:.4em}html.theme--catppuccin-latte .file.has-name.is-empty .file-name{display:none}html.theme--catppuccin-latte .file.is-boxed .file-label{flex-direction:column}html.theme--catppuccin-latte .file.is-boxed .file-cta{flex-direction:column;height:auto;padding:1em 3em}html.theme--catppuccin-latte .file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .label.is-large{font-size:1.5rem}html.theme--catppuccin-latte .help{display:block;font-size:.75rem;margin-top:0.25rem}html.theme--catppuccin-latte .help.is-white{color:#fff}html.theme--catppuccin-latte .help.is-black{color:#0a0a0a}html.theme--catppuccin-latte .help.is-light{color:#f5f5f5}html.theme--catppuccin-latte .help.is-dark,html.theme--catppuccin-latte .content kbd.help{color:#ccd0da}html.theme--catppuccin-latte .help.is-primary,html.theme--catppuccin-latte .docstring>section>a.help.docs-sourcelink{color:#1e66f5}html.theme--catppuccin-latte .help.is-link{color:#1e66f5}html.theme--catppuccin-latte .help.is-info{color:#179299}html.theme--catppuccin-latte .help.is-success{color:#40a02b}html.theme--catppuccin-latte .help.is-warning{color:#df8e1d}html.theme--catppuccin-latte .help.is-danger{color:#d20f39}html.theme--catppuccin-latte .field:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth .control{flex-grow:1;flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.is-grouped>.control{flex-shrink:0}html.theme--catppuccin-latte .field.is-grouped>.control:not(:last-child){margin-bottom:0;margin-right:.75rem}html.theme--catppuccin-latte .field.is-grouped>.control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.is-grouped.is-grouped-centered{justify-content:center}html.theme--catppuccin-latte .field.is-grouped.is-grouped-right{justify-content:flex-end}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline{flex-wrap:wrap}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:last-child,html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline>.control:not(:last-child){margin-bottom:0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:last-child{margin-bottom:-0.75rem}html.theme--catppuccin-latte .field.is-grouped.is-grouped-multiline:not(:last-child){margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field.is-horizontal{display:flex}}html.theme--catppuccin-latte .field-label .label{font-size:inherit}@media screen and (max-width: 768px){html.theme--catppuccin-latte .field-label{margin-bottom:0.5rem}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-label{flex-basis:0;flex-grow:1;flex-shrink:0;margin-right:1.5rem;text-align:right}html.theme--catppuccin-latte .field-label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.field-label{font-size:.75rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-normal{padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-medium{font-size:1.25rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-large{font-size:1.5rem;padding-top:0.375em}}html.theme--catppuccin-latte .field-body .field .field{margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-body{display:flex;flex-basis:0;flex-grow:5;flex-shrink:1}html.theme--catppuccin-latte .field-body .field{margin-bottom:0}html.theme--catppuccin-latte .field-body>.field{flex-shrink:1}html.theme--catppuccin-latte .field-body>.field:not(.is-narrow){flex-grow:1}html.theme--catppuccin-latte .field-body>.field:not(:last-child){margin-right:.75rem}}html.theme--catppuccin-latte .control{box-sizing:border-box;clear:both;font-size:1rem;position:relative;text-align:inherit}html.theme--catppuccin-latte .control.has-icons-left .input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input:focus~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-left .select:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right .input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input:focus~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input:focus~.icon,html.theme--catppuccin-latte .control.has-icons-right .select:focus~.icon{color:#ccd0da}html.theme--catppuccin-latte .control.has-icons-left .input.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-small~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-small~.icon{font-size:.75rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-medium~.icon{font-size:1.25rem}html.theme--catppuccin-latte .control.has-icons-left 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kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small 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.container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content 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ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v1.1.5/assets/themeswap.js b/v1.1.5/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/v1.1.5/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v1.1.5/assets/u.png b/v1.1.5/assets/u.png new file mode 100644 index 0000000000000000000000000000000000000000..59004243c142a1c367852c6147f9ab6bc62e97cd GIT binary patch literal 85926 zcmaI71yo$kvIdF;m*DOMcXtT{2^NC8>)`GK0RjYfcXxMpcXxMp80?Y%oO|zCXTA4k zt(obn{=Tm2s#o*Wg;sJM*Go*1%m>I27~-)frCMO{Gk224gS%l{y%-7IT+MG7%(uwkAE;Q$V~A6 zLuNw!PcOK1CglINt^NWnJ+$?}z#w+bmDC*7WMy~_ZLApejcg2z8C|Vx{{q1HU3ov6 zR>qF{B(7GL)(*U`0%ZRnct6^I)l6h0|3Dl80%U5kKS)Gv?2Sn{7}*(_$pqm^NJ#kY zjZAodii!W5{vipFnK?Sz@-i{GxVSL7urb=$n=-NR@bEA(vof)=GJGHy9NerO^<5dP z9mxMR$p4HZX6#^SZ*J>oZevaIcU*k~8z)BrGP1vh{`d1QKON0Y{?C%N!@sBXF+rxk 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zeMLKHFVp()kwe4hzwp7~#IX|!zw`ZXRG9X#N_xlp-Z1>y-}#WX_uScY!`t8c`r+4p z=Rxg{vuDl@KlAPfhQIk=epujV24MQ?H~y=S$ZsV*JDfgsdibe#-aq{2fBmuH$;Y3S zXID=TZI2JAC0E{POVBlh5h<_}=t0_YU{VOH9A_&4=Z3 z`Z*`GGg8oIJ6mKg#smzxPQw|3~#VM_%{lyNBQYy-y9iR-fM>dEiZV4}a$$ zeM*0mqm{JV#5{`C*EzxgV8&Hc9zKmWnEDE-Ept{;Bm?|yW6)g3qLoI&ny{_cl| z+wXp*!Y{k=+Tm~f?t{af_uMi(A#>!08?TY`|KLEopO86p!^^K3e)YFLINbBVZA!mR z=iCQ$&M~L1l{xo0nR5@wd0`GQ=RW-#@7J3T%t7Yd$3FX>;m1FGVmQW_lSzUPpZxXr zs(&`;-YetgzP0BZ    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v1.1.5/conventions/index.html b/v1.1.5/conventions/index.html new file mode 100644 index 00000000..382dc7cd --- /dev/null +++ b/v1.1.5/conventions/index.html @@ -0,0 +1,2 @@ + +Background and conventions · StartUpDG.jl

    Background

    Most high order finite element methods rely on a decomposition of a domain into a mesh of "elements" (e.g., triangles or quadrilaterals in 2D, hexahedra or tetrahedra in 3D). Each "physical" element in a mesh is assumed to be the image of single "reference" element under some geometric mapping. Using the chain rule and changes of variables, one can evaluate integrals and derivatives using only operations on the reference element and some geometric mapping data. This transformation of operations on all elements to a single reference element make finite element methods efficient.

    We use the convention that coordinates on the reference element are $r$ in 1D, $r, s$ in 2D, or $r, s, t$ in 3D. Physical coordinates use the standard conventions $x$, $x, y$, and $x, y, z$ in 1D, 2D, and 3D.

    Mapping

    Derivatives of reference coordinates with respect to physical coordinates are abbreviated, e.g., $\frac{\partial r}{\partial x} = r_x$. Additionally, $J$ is used to denote the determinant of the Jacobian of the reference-to-physical mapping.

    Assumptions

    We make a few simplifying assumptions about the mesh:

    • meshes are conforming (e.g., each face of an element is shared with at most one other element).
    • the geometric mapping from reference to physical elements is the same degree polynomial as the approximation space on the reference element (e.g., the mapping is isoparametric).

    Initial experimental support for hybrid, cut-cell, and non-conforming meshes in two dimensions is also available. Please see the corresponding test sets test/hybrid_mesh_tests.jl, test/cut_mesh_tests.jl, and noncon_mesh_tests.jl for examples.

    Code conventions

    StartUpDG.jl exports structs RefElemData{Dim, ElemShape, ...} (which contains data associated with the reference element, such as interpolation points, quadrature rules, face nodes, normals, and differentiation/interpolation/projection matrices) and MeshData{Dim} (which contains geometric data associated with a mesh). These are currently used for evaluating DG formulations in a matrix-free fashion. These structs contain fields similar to those in Globals1D, Globals2D, Globals3D in the NDG book codes.

    We use the following code conventions:

    • variables r, s, t and x, y, z correspond to values at nodal interpolation points.
    • variables ending in q (e.g., rq, sq,... and xq, yq,...) correspond to values at volume quadrature points.
    • variables ending in f (e.g., rf, sf,... and xf, yf,...) correspond to values at face quadrature points.
    • variables ending in p (e.g., rp, sp,...) correspond to equispaced plotting nodes.
    • Dr, Ds, Dt matrices are nodal differentiation matrices with respect to the $r, s, t$ coordinates. For example, Dr * f.(r, s) approximates the derivative of $f(r, s)$ at nodal points.
    • V matrices correspond to interpolation matrices from nodal interpolation points. For example, Vq interpolates to volume quadrature points, Vf interpolates to face quadrature points, Vp interpolates to plotting nodes.
    • geometric quantities in MeshData are stored as matrices of dimension $\text{number of points per element } \times \text{number of elements}$.

    Differences from the codes of "Nodal Discontinuous Galerkin Methods"

    The codes in StartUpDG.jl are based closely on the Matlab codes from the book "Nodal Discontinuous Galerkin Methods" by Hesthaven and Warburton (2008) (which we will refer to as "NDG"). However, there are some differences in order to allow for more general DG discretizations and enforce certain mathematical properties:

    • In NDG, Fmask extracts the interpolation nodes which lie on a face. These nodes are then used to compute interface fluxes. However, in StartUpDG.jl, we interpolate nodal values to values at face quadrature points via rd.Vf * u. These operations are equivalent if the interpolation nodes which lie on a face are co-located with quadrature points. Similarly, in NDG, the LIFT matrix maps face nodal points to volume nodal points. In StartUpDG.jl, the rd.LIFT matrix maps from face quadrature points to volume nodal points.
    • in NDG, there are connectivity arrays vmapM and vmapP, which directly retrieve interface values from arrays of nodal values. In StartUpDG.jl, face interpolation nodes are not guaranteed to be co-located with face quadrature nodes, so we do not provide vmapM and vmapP. Instead, we expect the user to compute face values and use the md.mapM, md.mapP arrays to access interface values.
    • in NDG, the mass matrix is computed exactly using the formula M = inv(VDM * VDM'), where VDM is the generalized Vandermonde matrix evaluated at nodal interpolation points. In StartUpDG.jl, the mass matrix is computed using quadrature. These are equivalent if the quadrature is exact for the integrands in the mass matrix (e.g., degree $2N$ polynomials for triangular or tetrahedral elements).
    • in NDG, the geometric terms rx, sx, ry, sy, ... are computed and stored. In StartUpDG.jl, the scaled geometric terms md.rxJ, md.sxJ, md.ryJ, md.syJ, ... are computed, which enable us to enforce the metric identities on curved meshes. Similarly, NDG provides Fscale = sJ ./ J(Fmask, :), while StartUpDG.jl only provides md.Jf, which is equivalent to sJ. Fscale, as well as the NDG geometric terms and can be recovered by dividing by md.J.

    Internally, NDG uses arrays EToE and EToF to compute the interface connectivity array mapP. StartUpDG.jl uses instead a face-to-face connectivity array FToF. However, EToE, EToF, and FToF are not typically required for the matrix-free explicit solvers targeted by this package.

    diff --git a/v1.1.5/ex_dg_deriv/index.html b/v1.1.5/ex_dg_deriv/index.html new file mode 100644 index 00000000..3dd20c99 --- /dev/null +++ b/v1.1.5/ex_dg_deriv/index.html @@ -0,0 +1,28 @@ + +Example: computing DG derivatives · StartUpDG.jl

    Example: approximating derivatives using DG

    MeshData can be used to compute DG derivatives. Suppose $f$ is a differentiable function and the domain $\Omega$ can be decomposed into non-overlapping elements $D^k$. The approximation of $\frac{\partial f}{\partial x}$ can be approximated using the following formulation: find piecewise polynomial $u$ such that for all piecewise polynomials $v$

    \[\int_{\Omega} u v = \sum_k \left( \int_{D^k} \frac{\partial u}{\partial x}v + \int_{\partial D^k} \frac{1}{2} \left[u\right]n_x v \right)\]

    Here, $\left[u\right] = u^+ - u$ denotes the jump across an element interface, and $n_x$ is the $x$-component of the outward unit normal on $D^k$.

    Discretizing the left-hand side of this formulation yields a mass matrix. Inverting this mass matrix to the right hand side yields the DG derivative. We show how to compute it for a uniform triangular mesh using MeshData and StartUpDG.jl.

    We first construct the triangular mesh and initialize md::MeshData.

    using StartUpDG
+using Plots
+
+N = 3
+K1D = 8
+rd = RefElemData(Tri(), N)
+VXY, EToV = uniform_mesh(Tri(), K1D)
+md = MeshData(VXY, EToV, rd)

    We can approximate a function $f(x, y)$ using interpolation

    f(x, y) = exp(-5 * (x^2 + y^2)) * sin(1 + pi*x) * sin(2 + pi*y)
+(; x, y) = md
+u = @. f(x, y)

    or using quadrature-based projection

    (; Pq ) = rd
+(; x, y, xq, yq ) = md
+u = Pq * f.(xq, yq)

    We can use scatter in Plots.jl to quickly visualize the approximation. This is not intended to create a high quality image (see other libraries, e.g., Makie.jl,VTK.jl, or Triplot.jl for publication-quality images).

    (; Vp ) = rd
+xp, yp, up = Vp * x, Vp * y, Vp * u # interp to plotting points
+scatter(xp, yp, uxp, zcolor=uxp, msw=0, leg=false, ratio=1, cam=(0, 90))

    Both interpolation and projection create a matrix u of size $N_p \times K$ which contains coefficients (nodal values) of the DG polynomial approximation to $f(x, y)$. We can approximate the derivative of $f(x, y)$ using the DG derivative formulation

    function dg_deriv_x(u, rd::RefElemData, md::MeshData)
+  (; Vf, Dr, Ds, LIFT ) = rd
+  (; rxJ, sxJ, J, nxJ, mapP ) = md
+  uf = Vf * u
+  ujump = uf[mapP] - uf
+
+  # derivatives using chain rule + lifted flux terms
+  ux = rxJ .* (Dr * u) + sxJ .* (Ds * u)  
+  dudxJ = ux + LIFT * (.5 * ujump .* nxJ)
+
+  return dudxJ ./ J
+end

    We can visualize the result as follows:

    dudx = dg_deriv_x(u, rd, md)
+uxp = Vp * dudx
+scatter(xp, yp, uxp, zcolor=uxp, msw=0, leg=false, ratio=1, cam=(0,90))

    Plots of the polynomial approximation $u(x,y)$ and the DG approximation of $\frac{\partial u}{\partial x}$ are given below

    u dudx ⠀

    diff --git a/v1.1.5/index.html b/v1.1.5/index.html new file mode 100644 index 00000000..432813b3 --- /dev/null +++ b/v1.1.5/index.html @@ -0,0 +1,20 @@ + +Home · StartUpDG.jl

    Overview

    This package contains routines to initialize reference element operators, physical mesh arrays, and connectivity arrays for nodal DG methods. The codes roughly based on Nodal Discontinuous Galerkin Methods by Hesthaven and Warburton (2007).

    A short example

    using StartUpDG
+
+# polynomial degree and mesh size
+N = 3
+K1D = 8
+
+# init ref element and mesh
+rd = RefElemData(Tri(), N)
+VXY, EToV = uniform_mesh(Tri(), K1D)
+md = MeshData(VXY, EToV, rd)
+
+# Define a function by interpolation
+(; x, y ) = md
+u = @. exp(-10 * (x^2 + y^2))
+
+# Compute derivatives using geometric mapping + chain rule
+(; Dr, Ds ) = rd
+(; rxJ, sxJ, J ) = md
+dudx = (rxJ .* (Dr * u) + sxJ .* (Ds * u)) ./ J
    diff --git a/v1.1.5/index_refs/index.html b/v1.1.5/index_refs/index.html new file mode 100644 index 00000000..79934a22 --- /dev/null +++ b/v1.1.5/index_refs/index.html @@ -0,0 +1,105 @@ + +Reference · StartUpDG.jl

    Index

    Functions

    StartUpDG.BoundaryTagPlotter — Type
    BoundaryTagPlotter(triout::TriangulateIO)

    Plot recipe to visualize boundary tags by color. Usage: plot(BoundaryTagPlotter(triout))

    source
    StartUpDG.CurvedMesh — Type
    struct CurvedMesh{T}

    Mesh type indicating that the mesh has been curved. Stores the original mesh type as a field.

    Fields

    originalmeshtype :: T

    source
    StartUpDG.CutCellMesh — Type

    CutCellMesh is used in the MeshData field mesh_type for cut cell meshes.

    The field physical_frame_elements is a container with shifting/scaling information for each element. We evaluate the physical basis over each element by applying a shifting and scaling of the physical coordinates. The resulting shifted/scaled coordinates then fall into the reference element and can be used to evaluate a reference element basis.

    The field cut_face_nodes is a container whose elements are indices of face nodes for a cut element. In other words, md.xf.cut[cut_face_nodes[1]] returns the face nodes of the first element.

    We assume all cut elements have the same number of volume quadrature points (which is at least the dimension of a degree 2N polynomial space).

    The field objects contains a tuple of the objects used to define the cut region.

    The field cut_cell_operators contains optionally precomputed operators (mass, differntiation, face interpolation, and lifting operators).

    The field cut_cell_data contains additional data from PathIntersections.

    source
    StartUpDG.MeshData — Type
    MeshData(rd::RefElemData, objects, 
+         vx::AbstractVector, vy::AbstractVector,
+         quadrature_type=Subtriangulation(); 
+         quad_rule_face=get_1d_quadrature(rd), 
+         precompute_operators=false)

    Constructor for MeshData utilizing moment fitting. Does not guarantee positive quadrature weights, and is slower due to the use of adaptive sampling to construct

    !!! Warning: this may be deprecated or removed in future versions.

    source
    StartUpDG.MeshData — Type
    struct MeshData{Dim, Tv, Ti}

    MeshData: contains info for a high order piecewise polynomial discretization on an unstructured mesh.

    Example:

    N, K1D = 3, 2
+rd = RefElemData(Tri(), N)
+VXY, EToV = uniform_mesh(Tri(), K1D)
+md = MeshData(VXY, EToV, rd)
+(; x, y ) = md
    source
    StartUpDG.MeshData — Method
    MeshData(VXYZ, EToV, rd::RefElemData)
+MeshData((VXYZ, EToV), rd::RefElemData)

    Returns a MeshData struct with high order DG mesh information from the unstructured mesh information (VXYZ..., EToV).

    MeshData(rd::RefElemData, md::MeshData, xyz...)

    Given new nodal positions xyz... (e.g., from mesh curving), recomputes geometric terms and outputs a new MeshData struct. Only fields modified are the coordinate-dependent terms xyz, xyzf, xyzq, rstxyzJ, J, nxyzJ, Jf.

    source
    StartUpDG.MeshImportOptions — Type
    MeshImportOptions

    This struct allows the user to opt for supported features when importing a Gmsh 4.1 .msh file.

    Support

    • grouping::Bool | On import would you like to include physical group assignements of 2D elements?
    • remap_group_name::Bool | On import would you like to maintain or remap physical group ID? Remap results in groupIds in the range 1:number_group_ids.
    source
    StartUpDG.MeshPlotter — Type
    MeshPlotter(rd::RefElemData, md::RefElemData)

    Plot recipe to plot a (possibly curved) quadrilateral or triangular mesh. Usage: plot(MeshPlotter(...))

    source
    StartUpDG.MultidimensionalQuadrature — Type
    MultidimensionalQuadrature

    A type parameter for Polynomial indicating that the quadrature has no specific structure. Example usage: 

    # these are both equivalent
+approximation_type = Polynomial{MultidimensionalQuadrature}() 
+approximation_type = Polynomial(MultidimensionalQuadrature())
    source
    StartUpDG.MultipleRefElemData — Type
    struct MultipleRefElemData{T <: NamedTuple}
+    data::T
+end

    Holds multiple RefElemData objects in data where typeof(data) <: NamedTuple.

    Individual RefElemData can be accessed via getproperty, for example rds.Tri.

    source
    StartUpDG.NamedArrayPartition — Type
    NamedArrayPartition(; kwargs...)
+NamedArrayPartition(x::NamedTuple)

    Similar to an ArrayPartition but the individual arrays can be accessed via the constructor-specified names. However, unlike ArrayPartition, each individual array must have the same element type.

    source
    StartUpDG.NonConformingMesh — Type
    Experimental implementation

    This is an experimental feature and may change without warning in future releases.

    This is a proof of concept implementation of a non-conforming mesh in StartUpDG.jl. The intended usage is as follows:

    rd = RefElemData(Quad(), N=7)
+md = MeshData(NonConformingQuadMeshExample(), rd)
+
+(; x, y) = md
+u = @. sin(pi * x) * sin(pi * y)
+
+# interpolate to faces
+num_total_faces = num_faces(rd.element_type) * md.num_elements
+uf = reshape(rd.Vf * u, :, num_total_faces)
+
+# interpolate faces to mortars (`uf` denotes mortar faces for `NonConformingMesh` types)
+(; nonconforming_faces, mortar_interpolation_matrix) = md.mesh_type
+
+u_mortar = reshape(mortar_interpolation_matrix * uf[:, nonconforming_faces], :, 2 * length(nonconforming_faces))
+
+# construct interior (uM = u⁻ "minus") values and exterior (uP = u⁺ "plus") values
+uM = hcat(uf, u_mortar) # uM = both element faces and mortar faces
+uP = uM[md.mapP]

    The mortar_projection_matrix similarly maps values from 2 mortar faces back to values on the original non-conforming face. These can be used to create DG solvers on non-conforming meshes.

    source
    StartUpDG.PhysicalFrame — Type
    `PhysicalFrame{NDIMS} <: AbstractElemShape{NDIMS}`

    PhysicalFrame element type. Uses a total degree N approximation space, but is computed with a tensor product Legendre basis as opposed to a triangular PKDO basis. Stores fields shifting and scaling to shift/scale physical coordinates so that they are on the reference element. 

    PhysicalFrame()
+PhysicalFrame(x, y)
+PhysicalFrame(x, y, vx, vy): stores coordinates `vx, vy` of background Cartesian cell

    Constructors for a PhysicalFrame object (optionally uses arrays of points x, y on a cut element).

    source
    StartUpDG.Polynomial — Type
    Polynomial{T}

    Represents polynomial approximation types (as opposed to finite differences). By default, Polynomial() constructs a Polynomial{StartUpDG.DefaultPolynomialType}. Specifying a type parameters allows for dispatch on additional structure within a polynomial approximation (e.g., collocation, tensor product quadrature, etc).

    source
    StartUpDG.RefElemData — Type
    struct RefElemData

    RefElemData: contains info (interpolation points, volume/face quadrature, operators) for a high order nodal basis on a given reference element.

    Example:

    N = 3
+rd = RefElemData(Tri(), N)
+(; r, s ) = rd
    source
    StartUpDG.RefElemData — Method
    RefElemData(elem; N, kwargs...)
+RefElemData(elem, approx_type; N, kwargs...)

    Keyword argument constructor for RefElemData (to "label" N via rd = RefElemData(Line(), N=3))

    source
    StartUpDG.RefElemData — Method
    RefElemData(elem::Line, approximation_type, N;
+            quad_rule_vol = quad_nodes(elem, N+1))
+RefElemData(elem, approximation_type, N;
+            quad_rule_vol = quad_nodes(elem, N),
+            quad_rule_face = quad_nodes(face_type(elem), N))

    Constructor for RefElemData for different element types.

    source
    StartUpDG.RefElemData — Method
    RefElemData(elementType::Line, approxType::SBP, N)
+RefElemData(elementType::Quad, approxType::SBP, N)
+RefElemData(elementType::Hex,  approxType::SBP, N)
+RefElemData(elementType::Tri,  approxType::SBP, N)

    SBP reference element data for Quad(), Hex(), and Tri() elements.

    For Line(), Quad(), and Hex(), approxType is SBP{TensorProductLobatto}.

    For Tri(), approxType can be SBP{Kubatko{LobattoFaceNodes}}, SBP{Kubatko{LegendreFaceNodes}}, or SBP{Hicken}.

    source
    StartUpDG.RefElemData — Method
    RefElemData(elem::Pyr, 
+            approximation_type::Polynomial, N;
+            quad_rule_vol=quad_nodes(elem, N),
+            quad_rule_face_quad=quad_nodes(Quad(), N), 
+            quad_rule_face_tri=quad_nodes(Tri(), N), 
+            quad_rule_face=(quad_rule_face_quad, quad_rule_face_tri),
+            Nplot=10)

    Builds operators for pyramids.

    source
    StartUpDG.RefElemData — Method
    RefElemData(elem::Union{Line, Quad, Hex}, approximation_type::Polynomial{Gauss}, N)

    Builds a rd::RefElemData with (N+1)-point Gauss quadrature in each dimension.

    source
    StartUpDG.RefElemData — Method
    RefElemData(elem::Union{Tri, Tet, Pyr}, approx_type::Polynomial{<:TensorProductQuadrature}, N; kwargs...)
+RefElemData(elem::Union{Wedge}, 
+                 approx_type::Polynomial{<:TensorProductQuadrature}, N; 
+                 quad_rule_tri = stroud_quad_nodes(Tri(), 2 * N),
+                 quad_rule_line = gauss_quad(0, 0, N),
+                 kwargs...)

    Uses collapsed coordinate volume quadrature. Should be called via

    RefElemData(Tri(), Polynomial(TensorProductQuadrature()), N)
    source
    StartUpDG.RefElemData — Method
    RefElemData(elem::Wedge, approximation_type::Polynomial, N;
+            quad_rule_vol=quad_nodes(elem, N),
+            quad_rule_face_quad=quad_nodes(Quad(), N), 
+            quad_rule_face_tri=quad_nodes(Tri(), N), 
+            quad_rule_face=(quad_rule_face_quad, quad_rule_face_tri),
+            Nplot=10)

    Builds operators for prisms/wedges

    source
    StartUpDG.TensorProductQuadrature — Type
    TensorProductQuadrature{T}

    A type parameter to Polynomial indicating that the quadrature has a tensor product structure. Example usage: 

    # these are both equivalent
+approximation_type = Polynomial{TensorProductQuadrature}(gauss_quad(0, 0, 1)) 
+approximation_type = Polynomial(TensorProductQuadrature(gauss_quad(0, 0, 1)))
    source
    StartUpDG.VertexMappedMesh — Type
    struct VertexMappedMesh

    The default MeshData mesh type, represents a mesh which is defined purely by vertex locations and element-to-vertex connectivities. For example, these include affine triangular meshes or bilinear quadrilateral or trilinear hexahedral meshes.

    Fields

    element_type :: TE <: AbstractElemShape
    VXYZ :: TV
    EToV :: TEV

    source
    StartUpDG.VertexMeshPlotter — Type
    VertexMeshPlotter((VX, VY), EToV, fv)
+VertexMeshPlotter(triout::TriangulateIO)

    Plot recipe to plot a quadrilateral or triangular mesh. Usage: plot(VertexMeshPlotter(...))

    source
    NodesAndModes.equi_nodes — Method
    function NodesAndModes.equi_nodes(elem::PhysicalFrame, curve, N)

    Returns back Np(N) equally spaced nodes on the background quadrilateral corresponding to elem, with points inside of curve removed.

    source
    StartUpDG.MeshData_to_vtk — Function

    MeshDatatovtk(md, rd, dim, data, dataname, datatype, filename, writedata = false, equidist_nodes = true)

    Translate the given mesh into a vtk-file. md holds a MeshData object rd holds a reference element data/RefElemData of a TensorProductWedge data holds an array of arrays (of size num_nodes by num_elements) with plotting data dataname is an array of strings with name of the associated data write_data, flag if data should be written or not (e.g., if data is not written, only the mesh will be saved as output) equi_dist_nodes flag if points should be interpolated to equidstant nodes

    source
    StartUpDG.MeshData_to_vtk — Method
    MeshData_to_vtk(md, rd, dim, data, dataname, datatype, filename, write_data = false, equi_dist_nodes = true)

    Translate the given mesh into a vtk-file. md holds a MeshData object rd holds a reference element data/RefElemData object. data holds an array of arrays (of size num_nodes by num_elements) with plotting data dataname is an array of strings with name of the associated data write_data, flag if data should be written or not (e.g., if data is not written, only the mesh will be saved as output) equi_dist_nodes flag if points should be interpolated to equidstant nodes

    source
    StartUpDG.build_node_maps — Method
    build_node_maps(FToF, Xf)

    Intialize the connectivity table along all edges and boundary node tables of all elements. mapM - map minus (interior). mapP - map plus (exterior).

    Xf = (xf, yf, zf) and FToF is size (Nfaces * K) and FToF[face] = face neighbor

    mapM, mapP are size Nfp x (Nfaces*K)

    Examples

    julia> mapM, mapP, mapB = build_node_maps(FToF, (xf, yf))
    source
    StartUpDG.caratheodory_pruning_qr — Method
    caratheodory_pruning_qr(V, w_in)

    This performs Caratheodory pruning using a naive QR-based algorithm. Returns (w, inds), where inds denotes sub-selected indices for a reduced quadrature rule, and w is a vector of reduced positive weights.

    The original Matlab code this was based on was authored by Akil Narayan.

    source
    StartUpDG.ck45 — Method
    ck45()

    Returns coefficients rka,rkb,rkc for the 4th order 5-stage low storage Carpenter/Kennedy Runge Kutta method. Coefficients evolve the residual, solution, and local time, e.g.,

    Example

    for i in eachindex(rk4a, rk4b)
+    @. res = rk4a[i] * res + dt * rhs # i = RK stage
+    @. u  += rk4b[i] * res
+end
    source
    StartUpDG.connect_mesh — Method
    connect_mesh(EToV,fv)

    Inputs:

    • EToV is a num_elements by Nv matrix whose rows identify the Nv vertices

    which make up one of the num_elements elements.

    • fv (an array of arrays containing unordered indices of face vertices).

    Output: FToF, an length(fv) by num_elements index array containing face-to-face connectivity.

    source
    StartUpDG.connect_mesh — Method
    connect_mesh(rd, face_centroids, region_flags, cutcells; tol = 1e2 * eps())

    Connects faces of a cut mesh to each other, returns FToF such that face f is connected to FToF[f].

    Inputs:

    • rd::RefElemData
    • facecentroids = (facecentroidsx, facecentroidsy), where `facecentroids_x/y` are vectors of coordinates of face centroids
    • region_flags, cutcells are return arguments from PathIntersections.define_regions

    The keyword argument tol is the tolerance for matches between face centroids.

    source
    StartUpDG.construct_cut_surface_quadrature — Function
    construct_cut_surface_quadrature(N, cutcells, quad_rule_1D = gauss_quad(0, 0, N))

    Constructs cut surface quadrature using a degree N geometric mapping and a reference quadrature rule quad_rule_1D. Returns xf, yf, nxJ, nyJ, wf which are vectors, and face_node_indices, which is a Vector{Vector{Int}} of global face node indices (which index into xf.cut, yf.cut, etc) for each face of each cut element.

    On boundaries of cut cells, the surface quadrature is taken to be exact for degree N^2 + (N-1) polynomials. This ensures satisfaction of a weak GSBP property.

    source
    StartUpDG.construct_cut_volume_quadrature — Method
    construct_cut_volume_quadrature(N, cutcells; target_degree = 2 * N - 1)

    Constructs volume quadrature using subtriangulations of cut cells and Caratheodory pruning. The resulting quadrature is exact for polynomials of degree target_degree.

    We set target_degree to 2 * N - 1 by default, which is sufficient to ensure that ∫du/dx * v is integrated exactly so that integration by parts holds under the generated cut cell quadrature.

    source
    StartUpDG.estimate_h — Method
    estimate_h(rd::RefElemData, md::MeshData)
+estimate_h(e, rd::RefElemData, md::MeshData) # e = element index

    Estimates the mesh size via min sizeofdomain * |J|/|Jf|, since |J| = O(hᵈ) and |Jf| = O(hᵈ⁻¹).

    source
    StartUpDG.findline — Method

    findline(word::String, lines)

    Outputs the line number of word in lines.

    It is assumed that the word exists at least once in the file.

    source
    StartUpDG.get_boundary_face_labels — Method
    function get_boundary_face_labels(triout::TriangulateIO, md::MeshData{2})

    Find Triangle segment labels of boundary faces. Returns two arguments:

    • boundary_face_tags: tags of faces on the boundary
    • boundary_faces: list of faces on the boundary of the domain
    source
    StartUpDG.get_node_boundary_tags — Method
    function get_node_boundary_tags(triout::TriangulateIO,md::MeshData{2},rd::RefElemData{2,Tri})

    Computes node_tags = Nfp x Nfaces * num_elements array where each entry is a Triangulate.jl tag number.

    source
    StartUpDG.get_num_elements — Function

    returns the number of elements in a .msh file of a specified dimension

    Notes: Gmsh includes elements in a .msh file of multiple dimensions. We want a count of how many

    2D elements are in our file. This corisponds to the number of elements in our tri mesh.

    source
    StartUpDG.hex_vtk_order — Function
    hex_vtk_order(corner_verts, order, dim, skip = false)

    Compute the coordinates of a VTKLAGRANGEHEXAHEDRON of a hex of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_HEXHEDRON

    Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py

    VTK node numbering of a hexagon:

                8+------+7
+            /|     /|
+           / |    / |
+         5+------+6 |

    z | 4+–-|–+3 | y | / | / |/ |/ |/ 0–> x 1+–––+2

    source
    StartUpDG.hybridized_SBP_operators — Method
    function hybridized_SBP_operators(rd::RefElemData{DIMS})

    Constructs hybridized SBP operators given a RefElemData. Returns operators Qrsth..., VhP, Ph.

    source
    StartUpDG.hybridized_SBP_operators — Method
    hybridized_SBP_operators(md::MeshData{2, <:CutCellMesh})

    This constructs hybridized SBP operators using the approach taken in Chan (2019), "Skew-Symmetric Entropy Stable Modal Discontinuous Galerkin Formulations". https://doi.org/10.1007/s10915-019-01026-w

    This function returns hybridized_operators::Vector{Tuple{<:Matrix, <:Matrix}} and project_and_interp_operators, projection_operators, interpolation_operators, which are all Vector{<:Matrix}, where each entry corresponds to a cut element.

    source
    StartUpDG.make_periodic — Method
    make_periodic(md::MeshData{Dim}, is_periodic...) where {Dim}
+make_periodic(md::MeshData{Dim}, is_periodic = ntuple(x -> true, Dim)) where {Dim}
+make_periodic(md::MeshData, is_periodic = true)

    Returns new MeshData such that the node maps mapP and face maps FToF are now periodic. Here, is_periodic is a tuple of Bool indicating whether or not to impose periodic BCs in the x,y, or z coordinate.

    source
    StartUpDG.n_verts_between — Method
    n_verts_between(n, from, to, dim)

    Compute the coordinates of n equally distributed points between the points given by from and to. dim is the dimension of from and to. Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py

    source
    StartUpDG.quad_vtk_order — Function
    quad_vtk_order(corner_verts, order, dim, skip = false)

    Compute the coordinates of a VTKLAGRANGEQUAD of a quad of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_QUAD Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py

    source
    StartUpDG.read_Gmsh_2D — Method
    read_Gmsh_2D(filename, args...)

    Reads a 2D triangular Gmsh file. Mesh formats 2.2 and 4.1 supported. Returns (VX, VY), EToV.

    Examples

    VXY, EToV = read_Gmsh_2D("eulerSquareCylinder2D.msh") # v2.2 file format
+VXY, EToV = read_Gmsh_2D("test/testset_Gmsh_meshes/periodicity_mesh_v4.msh") # v4.1 file format
+
+# if MeshImportOptions.grouping=true, then a third variable `grouping` is returned
+VXY, EToV, grouping = read_Gmsh_2D("test/testset_Gmsh_meshes/periodicity_mesh_v4.msh", MeshImportOptions(true, false))
+VXY, EToV, grouping = read_Gmsh_2D("test/testset_Gmsh_meshes/periodicity_mesh_v4.msh", true) # same as above

    See also

    https://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format
    https://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format-version-2-0028Legacy0029

    source
    StartUpDG.read_Gmsh_2D_v2 — Method
    read_Gmsh_2D_v2(filename)

    Reads triangular GMSH 2D file format 2.2 0 8. Returns (VX, VY), EToV.

    Examples

    VXY, EToV = read_Gmsh_2D_v2("eulerSquareCylinder2D.msh")

    https://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format-version-2-0028Legacy0029

    source
    StartUpDG.read_Gmsh_2D_v4 — Function

    For brevity when grouping is the only supported feature.

    example: VXY, EToV, grouping = read_Gmsh_2D_v4("file.msh",true)
+example: VXY, EToV = read_Gmsh_2D_v4("file.msh",false)
    source
    StartUpDG.read_Gmsh_2D_v4 — Method
    function read_Gmsh_2D_v4(filename, options)

    reads triangular GMSH 2D .msh files.

    Output

    This depends on if grouping is opted for or not

    • returns: (VX, VY), EToV
    • returns: (VX, VY), EToV, grouping

    Supported formats and features:

    • version 4.1 'physical group support 'remap group ids

    grouping application

    When modeling the wave equation you might want wave speeds to vary across your domain. By assigning physical groups in Gmsh we can maintain such groupings upon importing the .msh file. Each imported element will be a member of a phyical group.

    VXY, EToV = read_Gmsh_2D_v4("eulerSquareCylinder2D.msh")
+VXY, EToV = read_Gmsh_2D_v4("eulerSquareCylinder2D.msh",false)
+VXY, EToV, grouping = read_Gmsh_2D_v4("eulerSquareCylinder2D.msh", true)
+
+option = MeshImportOption(true)
+VXY, EToV, grouping = read_Gmsh_2D_v4("eulerSquareCylinder2D.msh", option)

    https://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format

    Notes: the version 4 format has a more detailed block data format this leads to more complicated parser.

    source
    StartUpDG.refine — Function
    function refine(triout, h, href = h/2)

    Refinement of a previous mesh given the current mesh size h. Preserves boundary/volume tags.

    source
    StartUpDG.remap_element_grouping — Method

    remapelementgrouping!(eg::Vector{Int}) GMSH uses integers for naming conventions. This function remaps the Gmsh ids to a list of ids 1:numGroups. This just cleans up a little after Gmsh

    Example output

    remapelementgrouping([16,16,17,17]) -> [1,1,2,2]

    source
    StartUpDG.sort_by_axis — Method
    sort_by_axis(corner_verts)

    Given the points 'corner_verts' sort them in a lexicographical order and return the permutated points.

    source
    StartUpDG.sparse_low_order_SBP_operators — Method
    function sparse_low_order_SBP_operators(rd; factor=1.01)

    Constructs sparse low order SBP operators given a RefElemData. Returns operators Qrst..., E ≈ Vf * Pq that satisfy a generalized summation-by-parts (GSBP) property:

        `Q_i + Q_i^T = E' * B_i * E`

    factor is a scaling which determines how close a node must be to another node to be considered a neighbor.

    source
    StartUpDG.subcell_limiting_operators — Method
    Δrst, Rrst = subcell_limiting_operators(rd::RefElemData)

    Returns tuples of subcell limiting operators Drst = (Δr, Δs, ...) and R = (Rr, Rs, ...) such that for r where sum(r) = 0, sum(D * Diagonal(θ) * R * r) = 0 for any choice of θ. These operators are useful for conservative subcell limiting techniques (see https://doi.org/10.1016/j.compfluid.2022.105627 for an example of such an approach on tensor product elements).

    Sparse SBP operators used in an intermediate step when buidling these subcell limiting operators; by default, these operators are constructed using sparse_low_order_SBP_operators. To construct subcell limiting operators for a general SBP operator, one can use the following:

    Δ, R = subcell_limiting_operators(Q::AbstractMatrix; tol = 100 * eps())
    source
    StartUpDG.subtriangulated_cutcell_quadrature — Function
    subtriangulated_cutcell_quadrature(cutcell, rd_tri::RefElemData, 
+                                   r1D = gauss_lobatto_quad(0,0,rd_tri.N))

    Constructs a quadrature from subtriangulations. The degree of both the quadrature rule and isoparametric mapping are specified by rd_tri.

    The optional argument r1D specifies the nodal points used for constructing a curved mapping via interpolatory warp and blend.

    source
    StartUpDG.tag_boundary_faces — Method
    function tag_boundary_faces(md, boundary_name::Symbol = :entire_boundary)
+function tag_boundary_faces(md, boundary_list::Dict{Symbol, <:Function})

    When called without arguments, just returns Dict(:entire_boundary => boundary_faces)`.

    Example usage: 

    julia> rd = RefElemData(Tri(), N=1)
+julia> md = MeshData(uniform_mesh(Tri(), 2)..., rd)
+julia> on_bottom_boundary(x, y, tol = 1e-13) = abs(y+1) < tol
+julia> on_top_boundary(x, y, tol = 1e-13) = abs(y-1) < tol
+julia> tag_boundary_faces(Dict(:bottom => on_bottom_boundary,
+                               :top    => on_top_boundary), md)
    source
    StartUpDG.tag_boundary_faces — Method
    function tag_boundary_faces(triout::TriangulateIO,
+                            rd::RefElemData{2,Tri}, md::MeshData{2},
+                            boundary_list::Union{NamedTuple,Dict{Symbol,Int}})

    Here, boundary_list is a Dict (or NamedTuple) whose values are the boundary tags for a TriangulateIO mesh format. The output is a Dict or NamedTuple with keys given by boundary_list and values equal to vectors of faces on that given boundary.

    Example usage:

    julia> using Triangulate, StartUpDG
+julia> triout = scramjet()
+julia> rd = RefElemData(Tri(),N=1)
+julia> md = MeshData(triangulateIO_to_VXYEToV(triout)...,rd)
+julia> tag_boundary_faces(triout,rd,md, Dict(:wall=>1, :inflow=>2, :outflow=>3))
    source
    StartUpDG.triangle_vtk_order — Function
    triangle_vtk_order(corner_verts, order, dim, skip = false)

    Compute the coordinates of a VTK_LAGRANGE_TRIANGLE of a triangle or order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_TRIANGLE Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py

    source
    StartUpDG.uniform_mesh — Method
    uniform_mesh(elem::Line,Kx)
+uniform_mesh(elem::Tri,Kx,Ky)
+uniform_mesh(elem::Quad,Kx,Ky)
+uniform_mesh(elem::Hex,Kx,Ky,Kz)
+uniform_mesh(elem, K)

    Uniform Kx (by Ky by Kz) mesh on $[-1,1]^d$, where d is the spatial dimension. Returns (VX,VY,VZ), EToV. When only one K is specified, it assumes a uniform mesh with K elements in each coordinate direction.

    K can also be specified using a keyword argument K1D, e.g., uniform_mesh(elem; K1D = 16).

    source
    StartUpDG.vtk_order — Method
    vtk_order(elem::Hex, order)

    Construct all node-points of a VTKLAGRANGEHEXAHEDRON of order order. The corner-nodes are given by the reference hexahedron used by StartUpDG in the order defined by vtk.

    source
    StartUpDG.vtk_order — Method
    vtk_order(elem::Quad, order)

    Construct all node-points of a VTKLAGRANGEQUAD of order order. The corner-nodes are given by the reference quadrilateral used by StartUpDG in the order defined by vtk

    source
    StartUpDG.vtk_order — Method
    vtk_order(elem::Tri, order)

    Construct all node-points of a VTK_LAGRANGE_TRIANGLE of order order. The corner-nodes are given by the reference-triangle used by StartUpDG in the order defined by vtk

    source
    StartUpDG.vtk_order — Method
    vtk_order(elem::Wedge, order)

    Construct all node-points of a VTKLAGRANGEWEDGE of order order. The corner-nodes are given by the reference-wedge used by StartUpDG

    source
    StartUpDG.wedge_vtk_order — Method
    wedge_vtk_order(corner_verts, order, dim)

    Compute the coordinates of a VTKLAGRANGEWEDGE of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py

    source
    Triangulate.triangulate — Function
    function Triangulate.triangulate(triin::TriangulateIO, maxarea, minangle=20)

    Convenience routine to avoid writing out @sprintf each time. Returns a TriangulateIO object.

    source
    diff --git a/v1.1.5/more_meshes/index.html b/v1.1.5/more_meshes/index.html new file mode 100644 index 00000000..0bad4cd2 --- /dev/null +++ b/v1.1.5/more_meshes/index.html @@ -0,0 +1,52 @@ + +Additional mesh types · StartUpDG.jl

    Additional mesh types

    In addition to more "standard" mesh types, StartUpDG.jl also has experimental support for hybrid and cut-cell meshes. Both are currently restricted to two dimensional domains.

    Hybrid meshes

    Experimental implementation

    This is an experimental feature and may change in future releases.

    There is initial support for hybrid meshes in StartUpDG.jl. The following is a short example where we interpolate a polynomial and compute its derivative.

    rds = RefElemData((Tri(), Quad()), N = 3)
+
+# Simple hybrid mesh for testing
+#   1  7______8______9
+#      |      | 3  / |
+#      |   4  |  / 5 |
+#   0  4 ---- 5 ---- 6 
+#      |      |      |
+#      |   1  |   2  |
+#   -1 1 ---- 2 ---- 3
+#     -1      0      1
+VX = [-1; 0; 1; -1; 0; 1; -1; 0; 1]
+VY = [-1; -1; -1; 0; 0; 0; 1; 1; 1]
+EToV = [[1 2 4 5], [2 3 5 6], [5 8 9], [4 5 7 8], [9 6 5]]
+
+md = MeshData(VX, VY, EToV, rds)
+
+# test that the local derivatives of a polynomial recover the exact derivative
+(; x, y ) = md
+u = @. x^3 - x^2 * y + 2 * y^3
+dudx = @. 3 * x^2 - 2 * x * y
+
+# compute local derivatives
+(; rxJ, sxJ, J ) = md
+dudr, duds = similar(md.x), similar(md.x)
+dudr.Quad .= rds[Quad()].Dr * u.Quad
+duds.Quad .= rds[Quad()].Ds * u.Quad
+dudr.Tri .= rds[Tri()].Dr * u.Tri
+duds.Tri .= rds[Tri()].Ds * u.Tri
+
+@show norm(@. dudx - (rxJ * dudr + sxJ * duds) / J) # should be O(1e-14)

    The main difference in the representation of hybrid meshes compared with standard MeshData objects is the use of NamedArrayPartition arrays as storage for the geometric coordinates. These arrays have "fields" corresponding to the element type, for example

    md.x.Tri
+md.x.Quad

    but can still be indexed as linear arrays.

    The mapP field behaves similarly. If we interpolate the values of u for each element type to surface quadrature nodes, we can use mapP to linearly index into the array to find neighbors. 

    uf = similar(md.xf)
+uf.Quad .= rds.Quad.Vf * u.Quad
+uf.Tri .= rds.Tri.Vf * u.Tri
+uf[md.mapP] # this returns the exterior node values

    Cut Meshes

    Experimental implementation

    This is an experimental feature and may change in future releases.

    Initial support for cut-cell meshes is available via PathIntersections.jl. By passing in a tuple of curves (defined as parametrized functions of one coordinate, see PathIntersections.jl documentation for more detail), StartUpDG.jl can compute a MeshData for a cut-cell mesh. 

    circle = PresetGeometries.Circle(R=0.33, x0=0, y0=0)
+cells_per_dimension_x, cells_per_dimension_y = 4, 4
+
+rd = RefElemData(Quad(), N=3)
+md = MeshData(rd, (circle, ), cells_per_dimension_x, cells_per_dimension_y, Subtriangulation(); precompute_operators=true)

    Here, the final argument quadrature_type = Subtriangulation() determines how the quadrature on cut cells is determined. For Subtriangulation(), the quadrature on cut cells is constructed from a curved isoparametric subtriangulation of the cut cell. The number of quadrature points on a cut cell is then reduced (while preserving positivity) using Caratheodory pruning. If not specified, the quadrature_type argument defaults to Subtriangulation().

    Quadrature rules can also be constructed by specifying quadrature_type = MomentFitting(). The quadrature points on cut cells md.xq.cut are determined from sampling and a pivoted QR decomposition. This is not recommended, as it can be both slower, and the cut-cell quadrature weights md.wJq.cut are not guaranteed to be positive.

    The interpolation points on cut cells md.x.cut are determined from sampled points and a pivoted QR decomposition.

    The optional keyword argument precompute_operators specifies whether to precompute differentiation, face interpolation, mass, and lifting matrices for each cut cell. If precompute_operators=true, these are stored in md.mesh_type.cut_cell_operators.

    As with hybrid meshes, the nodal coordinates md.x, md.y are NamedArrayPartitions with cartesian and cut fields. For example, md.x.cartesian and md.x.cut are the x-coordinates of the Cartesian and cut cells, respectively. Likewise, md.mapP indexes linearly into the array of face coordinates and specifies exterior node indices. For example, we can interpolate a function to face nodes and compute exterior values via the following code:

    (; x, y) = md
+u = @. x^rd.N - x * y^(rd.N-1) - x^(rd.N-1) * y + y^rd.N # some random function 
+
+# interpolate the solution to face nodes
+uf = similar(md.xf) 
+uf.cartesian .= rd.Vf * u.cartesian
+for e in 1:size(md.x.cut, 2)
+    ids = md.mesh_type.cut_face_nodes[e]
+    Vf = md.mesh_type.cut_cell_operators.face_interpolation_matrices[e]
+    uf.cut[ids] .= Vf * u.cut[:, e]
+end
+
+uf[md.mapP] # these are "exterior" values for each entry of `uf`
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All elements of xyz are N_p times N_rm elements matrices, where N_p are the number of nodal points on each element.\nxyzq::NTuple{Dim, ...}, wJq: volume quadrature points/weights mapped to physical elements. All elements these tuples are N_q times N_rm elements matrices, where N_q is the number of quadrature points on each element.\nxyzf::NTuple{Dim, ...}: face quadrature points mapped to physical elements. All elements of xyz are N_f times N_rm elements matrices, where N_f is the number of face points on each element.\nmapP, mapB: indexing arrays for inter-element node connectivity (mapP) and for extracting boundary nodes from the list of face nodes xyzf (mapB). mapP is a matrix of size N_f times N_rm elements, while the length of mapB is the total number of nodes on the boundary.\nrstxyzJ::SMatrix{Dim, Dim}: volume geometric terms G_ij = fracpartial x_ipartial hatx_j. Each element of rstxyzJ is a matrix of size N_p times N_rm elements.\nJ, Jf: volume and surface Jacobians evaluated at interpolation points and surface quadrature points, respectively. J is a matrix of size N_p times N_rm elements, while Jf is a matrix of size N_f times N_rm elements. \nnxyz::NTuple{Dim, ...} and nxyzJ::NTuple{Dim, ...}: normalized and Jf scaled outward normals evaluated at surface quadrature points. Each element of nxyzJ is a matrix of size N_f times N_rm elements. ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"These are the main quantities used to construct a DG solver. Information specific to the type of mesh used is stored in the md.mesh_type field. ","category":"page"},{"location":"MeshData/#Setting-up-md::MeshData","page":"MeshData","title":"Setting up md::MeshData","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"The MeshData struct contains data for high order DG methods useful for evaluating DG formulations in a matrix-free fashion.","category":"page"},{"location":"MeshData/#Generating-unstructured-meshes","page":"MeshData","title":"Generating unstructured meshes","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"For convenience, simple uniform meshes are included in with StartUpDG.jl via uniform_mesh","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"using StartUpDG\nnum_cells_x, num_cells_y, num_cells_z = 4, 2, 8\n(VX,), EToV = uniform_mesh(Line(), num_cells_x)\n(VX, VY), EToV = uniform_mesh(Tri(), num_cells_x, num_cells_y)\n(VX, VY), EToV = uniform_mesh(Quad(), num_cells_x, num_cells_y)\n(VX, VY, VZ), EToV = uniform_mesh(Tet(), num_cells_x, num_cells_y, num_cells_z)\n(VX, VY, VZ), EToV = uniform_mesh(Pyr(), num_cells_x, num_cells_y, num_cells_z)\n(VX, VY, VZ), EToV = uniform_mesh(Wedge(), num_cells_x, num_cells_y, num_cells_z)\n(VX, VY, VZ), EToV = uniform_mesh(Hex(), num_cells_x, num_cells_y, num_cells_z)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"The uniform triangular mesh is constructed by creating a uniform quadrilateral mesh then bisecting each quad into two triangles. Wedge meshes are constructed similarly. Tet meshes are constructed by dividing each hexahedron into 5 tetrahedral elements. Pyramid meshes are constructed by dividing each hexahedron into 6 pyramids. ","category":"page"},{"location":"MeshData/#Initializing-high-order-DG-mesh-data","page":"MeshData","title":"Initializing high order DG mesh data","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"Given unstructured mesh information (tuple of vertex coordinates VXYZ and index array EToV) high order DG mesh data can be constructed as follows:","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"md = MeshData(VXYZ, EToV, rd)","category":"page"},{"location":"MeshData/#Enforcing-periodic-boundary-conditions","page":"MeshData","title":"Enforcing periodic boundary conditions","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"Periodic boundary conditions can be enforced via the is_periodic keyword argument ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"md_periodic = MeshData((VX, VY), EToV, rd; is_periodic=true) # periodic in both x and y coordinates\nmd_periodic_x = MeshData((VX, VY), EToV, rd; is_periodic=(true, false)) # periodic in x direction, but not y","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"or by calling make_periodic, which returns a new MeshData instance","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"md = MeshData((VX, VY), EToV, rd)\nmd_periodic = make_periodic(md) # periodic in both x and y coordinates\nmd_periodic_x = make_periodic(md, true, false) # periodic in x direction, but not y","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"In either case, the MeshData indexing arrays fields mapP,mapB, and FToF are modified to account for periodicity.","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"One can check which dimensions are periodic via the is_periodic field of MeshData. For example, the md_periodic_x example above gives","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"julia> md_periodic_x.is_periodic\n(true, false)","category":"page"},{"location":"MeshData/#Creating-curved-meshes","page":"MeshData","title":"Creating curved meshes","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"It is common to generate curved meshes by first generating a linear mesh, then moving high order nodes on the linear mesh. This can be done by calling MeshData again with new x, y coordinates:","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"md = MeshData((VX, VY), EToV, rd)\n(; x, y ) = md\n# <-- code to modify high order nodes (x,y)\nmd_curved = MeshData(rd, md, x, y)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"MeshData(rd, md, x, y) and MeshData(rd, md, x, y, z) are implemented for 2D and 3D, though this is not currently implemented in 1D.","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"More generally, one can create a copy of a MeshData with certain fields modified by using @set or setproperties from Setfield.jl.","category":"page"},{"location":"MeshData/#Unstructured-and-pre-defined-triangular-meshes-using-Triangulate.jl","page":"MeshData","title":"Unstructured and pre-defined triangular meshes using Triangulate.jl","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"StartUpDG.jl also includes additional utilities based on Triangulate.jl for creating and visualizing meshes. Several pre-defined geometries are included in StartUpDG.jl. A few examples are SquareDomain, RectangularDomainWithHole, Scramjet, and CircularDomain. See triangulate_example_meshes.jl for a more complete list and field arguments. These can each be called using triangulate_domain, for example the following code will create a mesh of a scramjet:","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"meshIO = triangulate_domain(Scramjet())\n(VX, VY), EToV = triangulateIO_to_VXYEToV(meshIO)\nrd = RefElemData(Tri(), 7)\nmd = MeshData((VX, VY), EToV, rd)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"A quick plot of the face nodes via ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"using Plots\nscatter(vec.(md.xyzf)..., msw=0, ms=1, aspect_ratio=:equal, ylims=(0,2), leg=false)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"shows the following figure (Image: u)","category":"page"},{"location":"MeshData/#Unstructured-curved-quadrilateral-and-hexahedral-meshes-using-HOHQMesh.jl","page":"MeshData","title":"Unstructured curved quadrilateral and hexahedral meshes using HOHQMesh.jl","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"StartUpDG.jl also reads in .mesh files generated by HOHQMesh.jl. The following code constructs a MeshData which represents a curved quadrilateral mesh generated by HOHQMesh.jl. ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"using StartUpDG\nrd = RefElemData(Quad(), 4)\nhmd = read_HOHQMesh(\"test/testset_HOHQMesh_meshes/easy_example.mesh\", Quad())\nmd = MeshData(hmd, rd)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"We can visualize the mesh using ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"using Plots\nplot(rd, md) # can also use `plot(MeshPlotter(rd, md))`","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"which yields the following figure:","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"(Image: u)","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"The boundary faces are also automatically tagged with the labels provided in the HOHQMesh file. Each boundary tag and the faces that lie on it are stored in md.mesh_type.boundary_faces. ","category":"page"},{"location":"MeshData/#Tagging-boundary-faces-and-boundary-nodes","page":"MeshData","title":"Tagging boundary faces and boundary nodes","text":"","category":"section"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"One can \"tag\" boundary faces (or boundary nodes) by specifying boolean functions which evaluate to true if a point is on a given boundary segment. ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"rd = RefElemData(Tri(), N=3)\nmd = MeshData(uniform_mesh(Tri(), 1)..., rd)\non_bottom_boundary(point, tol=1e-13) = abs(point[2] + 1) < tol # point = (x,y)\non_top_boundary(point, tol=1e-13) = abs(point[2] - 1) < tol \n\nboundary_face_dict = tag_boundary_faces(md, Dict(:bottom => on_bottom_boundary, :top => on_top_boundary))\nboundary_node_dict = tag_boundary_nodes(rd, md, Dict(:bottom => on_bottom_boundary, :top => on_top_boundary))","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"You can also specify a list of boundaries using NamedTuples ","category":"page"},{"location":"MeshData/","page":"MeshData","title":"MeshData","text":"boundary_face_dict = tag_boundary_faces(md, (; :bottom=>on_bottom_boundary,:top=>on_top_boundary))\nboundary_node_dict = tag_boundary_nodes(rd, md, (; :bottom=>on_bottom_boundary,:top=>on_top_boundary))","category":"page"},{"location":"RefElemData/#RefElemData-type","page":"RefElemData","title":"RefElemData type","text":"","category":"section"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"RefElemData contains the following fields","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"element_type::AbstractElemShape: element shape. Line, Tri, Quad, Hex, Wedge, Pyr, Tet currently supported.\napproximation_type: approximation type. Defaults to Polynomial(), but SBP() is also supported (see RefElemData based on SBP finite differences).\nNfaces: number of faces on a given type of reference element.\nfv: list of vertices defining faces, e.g., [1,2], [2,3], [3,1] for a triangle\nFmask: indices of interpolation nodes which lie on the faces\nVDM: the generalized Vandermonde matrix, a square matrix whose columns are V_ij = phi_j(x_i, where phi_j are orthonormal basis functions and x_i are interpolation points.\nrst::NTuple{Dim, ...}: tuple of vectors of length N_p, each of which contains coordinates of degree N optimized polynomial interpolation points.\nrstq::NTuple{Dim, ...},wq, Vq: tuple of volume quadrature points, vector of weights, and quadrature interpolation matrix. Each element of rstq and wq are vectors of length N_q, and Vq is a matrix of size N_q times N_p.\nN_{\\rm plot}: the degree which determines the number of plotting points N_prm plot.\nrstp::NTuple{Dim, ...}, Vp: tuple of plotting points and plotting interpolation matrix. Each element of rstp is a vector of length N_prm plot, and Vp is a matrix of size N_prm plot times N_p.\nrstf::NTuple{Dim, ...},wf, Vf: tuple of face quadrature points, weights, and face interpolation matrix. Each element of rstf and wf are vectors of length N_f, and Vf is a matrix of size N_f times N_p.\nnrstJ::NTuple{Dim, ...}: tuple of outward reference normals, scaled by the face Jacobian. Each element is a vector of length N_f.\nM: mass matrix computed using quadrature. Size N_p times N_p\nPq: quadrature-based L^2 projection matrix. Size N_p times N_q.\nDrst::NTuple{Dim, ...}, LIFT: differentiation and lifting matrices. Differentiation matrices are size N_p times N_p while lift matrices are size N_ptimes N_f.","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"This list is incomplete; other fields are stored or accessible but currently only used for internal computations.","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"Mass, differentiation, lifting, and interpolation matrices can be specialized. For example, these matrices are dense Matrix{T} type for lines and triangles, but could also be stored as sparse matrices for quadrilaterals and hexahedra.","category":"page"},{"location":"RefElemData/#Setting-up-rd::RefElemData","page":"RefElemData","title":"Setting up rd::RefElemData","text":"","category":"section"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"The struct rd::RefElemData contains data for a given element type. All common reference elements are supported: Line, Tri, Quad, Tet, Pyr, Wedge, and Hex.","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"To initalize a RefElemData, just specify the element type and polynomial degree.","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"N = 3\n\n# 1D elements \nrd = RefElemData(Line(), N)\n\n# 2D elements\nrd = RefElemData(Tri(), N)\nrd = RefElemData(Quad(), N)\n\n# 3D elements\nrd = RefElemData(Tet(), N)\nrd = RefElemData(Pyr(), N)\nrd = RefElemData(Wedge(), N)\nrd = RefElemData(Hex(), N)","category":"page"},{"location":"RefElemData/#Specifying-different-quadrature-rules.","page":"RefElemData","title":"Specifying different quadrature rules.","text":"","category":"section"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"By default, RefElemData initializes volume and surface quadrature rules to be the minimum rules which exactly integrate the unweighted volume and surface mass matrices. If different quadrature rules are desired, they can be specified as follows: ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"N = 3\n\n# create degree N tensor product Gauss-Lobatto rule\nr1D, w1D = gauss_lobatto_quad(0, 0, N)\nrq, sq = vec.(StartUpDG.meshgrid(r1D))\nwr, ws = vec.(StartUpDG.meshgrid(w1D))\nwq = @. wr * ws\n\nrd = RefElemData(Quad(), N; quad_rule_vol = (rq, sq, wq), \n quad_rule_face = (r1D, w1D))","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"This results in a DG spectral element method (DG-SEM) discretization, with a diagonal lumped mass matrix and differentiation matrices which satisfy a summation-by-parts property. ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"By default, RefElemData is constructed for a nodal basis (in order to facilitate curved meshes, connectivity, etc). The interpolation nodes are computed using an interpolatory version of the warp-and-blend procedure. ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"note: Note\nWhile specifying the quadrature rule changes the discretization, it is not reflected in the RefElemData type and thus cannot be specialized on. The following constructors produce RefElemData where the quadrature structure is reflected in the type parameters:rd = RefElemData(Hex(), Polynomial(TensorProductQuadrature(quad_nodes(Line(), N+1)), N)) # tensor product quadrature rules\nrd = RefElemData(Quad(), Polynomial{Gauss}(), N) # (N+1)^d point tensor product Gauss quadrature","category":"page"},{"location":"RefElemData/#RefElemData-based-on-SBP-finite-differences","page":"RefElemData","title":"RefElemData based on SBP finite differences","text":"","category":"section"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"It is also possible to construct a RefElemData based on both traditional finite difference SBP operators and multi-dimensional SBP finite difference operators. The traditional finite difference SBP operators are built using SummationByPartsOperators.jl. The multi-dimensional SBP operators utilize nodes constructed by Tianheng Chen and Chi-Wang Shu, Ethan Kubatko, and Jason Hicken. ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"Some examples of traditional finite difference SBP operators on tensor product domains:","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"using StartUpDG\nusing SummationByPartsOperators # this package must be loaded to enable extension\n\nD = derivative_operator(MattssonNordström2004(), \n derivative_order=1, accuracy_order=N+1,\n xmin=-1.0, xmax=1.0, N=20)\n\nrd = RefElemData(Line(), D) \nrd = RefElemData(Quad(), D)\nrd = RefElemData(Hex(), D)","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"Some examples of multi-dimensional SBP operators:","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"N = 3\nrd = RefElemData(Quad(), SBP(), N) # defaults to SBP{TensorProductLobatto}\nrd = RefElemData(Quad(), SBP{TensorProductLobatto}(), N) \n\nrd = RefElemData(Hex(), SBP(), N) # defaults to SBP{TensorProductLobatto}\nrd = RefElemData(Hex(), SBP{TensorProductLobatto}(), N) \n\nrd = RefElemData(Tri(), SBP(), N) # defaults to SBP{Kubatko{LobattoFaceNodes}}\nrd = RefElemData(Tri(), SBP{Hicken}(), N) \nrd = RefElemData(Tri(), SBP{Kubatko{LobattoFaceNodes}}(), N) \nrd = RefElemData(Tri(), SBP{Kubatko{LegendreFaceNodes}}(), N) ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"Quadrature rules of both degree 2*N-1 (up to N = 6) and 2*N (up to N = 4) are supported on triangles. For Line, Quad, and Hex elements, RefElemData(..., SBP(), N) is the same as the RefElemData for a DG-SEM discretization, though some fields are specialized for the SBP type. These SBP-based RefElemData objects can also be used to initialize a mesh (for example, md = MeshData(uniform_mesh(rd.element_type, 4)..., rd)). ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"On triangles, we have the following SBP types with the following properties:","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"SBP{Kubatko{LobattoFaceNodes}}: degree 2N-1 accurate quadrature rules with N+2 Lobatto nodes on each face. Nodes for N=4: ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"(Image: klobatto4)","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"SBP{Kubatko{LegendreFaceNodes}}: degree 2N-1 accurate quadrature rules with N+1 Legendre nodes on each face. For N = 1,...,4, these are the same as the nodes constructed by Chen and Shu. Nodes for N=4:","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"(Image: klegendre4)","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"SBP{Hicken}: degree 2N accurate quadrature rules with N+2 Lobatto nodes on each face. Nodes for N=4:","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"(Image: hicken4)","category":"page"},{"location":"RefElemData/#Tensor-product-RefElemData-on-wedge-elements","page":"RefElemData","title":"Tensor product RefElemData on wedge elements","text":"","category":"section"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"warning: Experimental implementation\nThis is an experimental feature and may change in future releases.","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"There is experimental support for RefElemDatas created from tensor products of triangular and 1D RefElemData objects. ","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"line = RefElemData(Line(), N_line)\ntri = RefElemData(Tri(), N_tri)\nrd = RefElemData(Wedge(), TensorProductWedge(tri, line))","category":"page"},{"location":"RefElemData/","page":"RefElemData","title":"RefElemData","text":"This new rd::RefElemData can then be used to create a wedge-based MeshData. The individual RefElemData objects can be accessed from rd.approximation_type::TensorProductWedge. ","category":"page"},{"location":"conventions/#Background","page":"Background and conventions","title":"Background","text":"","category":"section"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"Most high order finite element methods rely on a decomposition of a domain into a mesh of \"elements\" (e.g., triangles or quadrilaterals in 2D, hexahedra or tetrahedra in 3D). Each \"physical\" element in a mesh is assumed to be the image of single \"reference\" element under some geometric mapping. Using the chain rule and changes of variables, one can evaluate integrals and derivatives using only operations on the reference element and some geometric mapping data. This transformation of operations on all elements to a single reference element make finite element methods efficient. ","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"We use the convention that coordinates on the reference element are r in 1D, r s in 2D, or r s t in 3D. Physical coordinates use the standard conventions x, x y, and x y z in 1D, 2D, and 3D. ","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"(Image: Mapping)","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"Derivatives of reference coordinates with respect to physical coordinates are abbreviated, e.g., fracpartial rpartial x = r_x. Additionally, J is used to denote the determinant of the Jacobian of the reference-to-physical mapping. ","category":"page"},{"location":"conventions/#Assumptions","page":"Background and conventions","title":"Assumptions","text":"","category":"section"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"We make a few simplifying assumptions about the mesh:","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"meshes are conforming (e.g., each face of an element is shared with at most one other element). \nthe geometric mapping from reference to physical elements is the same degree polynomial as the approximation space on the reference element (e.g., the mapping is isoparametric). ","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"Initial experimental support for hybrid, cut-cell, and non-conforming meshes in two dimensions is also available. Please see the corresponding test sets test/hybrid_mesh_tests.jl, test/cut_mesh_tests.jl, and noncon_mesh_tests.jl for examples. ","category":"page"},{"location":"conventions/#Code-conventions","page":"Background and conventions","title":"Code conventions","text":"","category":"section"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"StartUpDG.jl exports structs RefElemData{Dim, ElemShape, ...} (which contains data associated with the reference element, such as interpolation points, quadrature rules, face nodes, normals, and differentiation/interpolation/projection matrices) and MeshData{Dim} (which contains geometric data associated with a mesh). These are currently used for evaluating DG formulations in a matrix-free fashion. These structs contain fields similar to those in Globals1D, Globals2D, Globals3D in the NDG book codes. ","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"We use the following code conventions:","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"variables r, s, t and x, y, z correspond to values at nodal interpolation points. \nvariables ending in q (e.g., rq, sq,... and xq, yq,...) correspond to values at volume quadrature points. \nvariables ending in f (e.g., rf, sf,... and xf, yf,...) correspond to values at face quadrature points. \nvariables ending in p (e.g., rp, sp,...) correspond to equispaced plotting nodes.\nDr, Ds, Dt matrices are nodal differentiation matrices with respect to the r s t coordinates. For example, Dr * f.(r, s) approximates the derivative of f(r s) at nodal points. \nV matrices correspond to interpolation matrices from nodal interpolation points. For example, Vq interpolates to volume quadrature points, Vf interpolates to face quadrature points, Vp interpolates to plotting nodes. \ngeometric quantities in MeshData are stored as matrices of dimension textnumber of points per element times textnumber of elements.","category":"page"},{"location":"conventions/#Differences-from-the-codes-of-\"Nodal-Discontinuous-Galerkin-Methods\"","page":"Background and conventions","title":"Differences from the codes of \"Nodal Discontinuous Galerkin Methods\"","text":"","category":"section"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"The codes in StartUpDG.jl are based closely on the Matlab codes from the book \"Nodal Discontinuous Galerkin Methods\" by Hesthaven and Warburton (2008) (which we will refer to as \"NDG\"). However, there are some differences in order to allow for more general DG discretizations and enforce certain mathematical properties:","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"In NDG, Fmask extracts the interpolation nodes which lie on a face. These nodes are then used to compute interface fluxes. However, in StartUpDG.jl, we interpolate nodal values to values at face quadrature points via rd.Vf * u. These operations are equivalent if the interpolation nodes which lie on a face are co-located with quadrature points. Similarly, in NDG, the LIFT matrix maps face nodal points to volume nodal points. In StartUpDG.jl, the rd.LIFT matrix maps from face quadrature points to volume nodal points. \nin NDG, there are connectivity arrays vmapM and vmapP, which directly retrieve interface values from arrays of nodal values. In StartUpDG.jl, face interpolation nodes are not guaranteed to be co-located with face quadrature nodes, so we do not provide vmapM and vmapP. Instead, we expect the user to compute face values and use the md.mapM, md.mapP arrays to access interface values. \nin NDG, the mass matrix is computed exactly using the formula M = inv(VDM * VDM'), where VDM is the generalized Vandermonde matrix evaluated at nodal interpolation points. In StartUpDG.jl, the mass matrix is computed using quadrature. These are equivalent if the quadrature is exact for the integrands in the mass matrix (e.g., degree 2N polynomials for triangular or tetrahedral elements).\nin NDG, the geometric terms rx, sx, ry, sy, ... are computed and stored. In StartUpDG.jl, the scaled geometric terms md.rxJ, md.sxJ, md.ryJ, md.syJ, ... are computed, which enable us to enforce the metric identities on curved meshes. Similarly, NDG provides Fscale = sJ ./ J(Fmask, :), while StartUpDG.jl only provides md.Jf, which is equivalent to sJ. Fscale, as well as the NDG geometric terms and can be recovered by dividing by md.J. ","category":"page"},{"location":"conventions/","page":"Background and conventions","title":"Background and conventions","text":"Internally, NDG uses arrays EToE and EToF to compute the interface connectivity array mapP. StartUpDG.jl uses instead a face-to-face connectivity array FToF. However, EToE, EToF, and FToF are not typically required for the matrix-free explicit solvers targeted by this package. ","category":"page"},{"location":"index_refs/#Index","page":"Reference","title":"Index","text":"","category":"section"},{"location":"index_refs/","page":"Reference","title":"Reference","text":"","category":"page"},{"location":"index_refs/#Functions","page":"Reference","title":"Functions","text":"","category":"section"},{"location":"index_refs/","page":"Reference","title":"Reference","text":"Modules = [StartUpDG]","category":"page"},{"location":"index_refs/#StartUpDG.BoundaryTagPlotter","page":"Reference","title":"StartUpDG.BoundaryTagPlotter","text":"BoundaryTagPlotter(triout::TriangulateIO)\n\nPlot recipe to visualize boundary tags by color. Usage: plot(BoundaryTagPlotter(triout))\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.CurvedMesh","page":"Reference","title":"StartUpDG.CurvedMesh","text":"struct CurvedMesh{T}\n\nMesh type indicating that the mesh has been curved. Stores the original mesh type as a field.\n\nFields\n\noriginalmeshtype :: T\n\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.CutCellMesh","page":"Reference","title":"StartUpDG.CutCellMesh","text":"CutCellMesh is used in the MeshData field mesh_type for cut cell meshes.\n\nThe field physical_frame_elements is a container with shifting/scaling information for each element. We evaluate the physical basis over each element by applying a shifting and scaling of the physical coordinates. The resulting shifted/scaled coordinates then fall into the reference element and can be used to evaluate a reference element basis. \n\nThe field cut_face_nodes is a container whose elements are indices of face nodes for a cut element. In other words, md.xf.cut[cut_face_nodes[1]] returns the face nodes of the first element. \n\nWe assume all cut elements have the same number of volume quadrature points (which is at least the dimension of a degree 2N polynomial space). \n\nThe field objects contains a tuple of the objects used to define the cut region.\n\nThe field cut_cell_operators contains optionally precomputed operators (mass, differntiation, face interpolation, and lifting operators). \n\nThe field cut_cell_data contains additional data from PathIntersections.\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MeshData","page":"Reference","title":"StartUpDG.MeshData","text":"MeshData(rd::RefElemData, objects, \n vx::AbstractVector, vy::AbstractVector,\n quadrature_type=Subtriangulation(); \n quad_rule_face=get_1d_quadrature(rd), \n precompute_operators=false)\n\nConstructor for MeshData utilizing moment fitting. Does not guarantee positive quadrature weights, and is slower due to the use of adaptive sampling to construct \n\n!!! Warning: this may be deprecated or removed in future versions. \n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MeshData-2","page":"Reference","title":"StartUpDG.MeshData","text":"struct MeshData{Dim, Tv, Ti}\n\nMeshData: contains info for a high order piecewise polynomial discretization on an unstructured mesh. \n\nExample:\n\nN, K1D = 3, 2\nrd = RefElemData(Tri(), N)\nVXY, EToV = uniform_mesh(Tri(), K1D)\nmd = MeshData(VXY, EToV, rd)\n(; x, y ) = md\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MeshData-Tuple{Tuple{Tuple, Matrix{Int64}}, RefElemData, Vararg{Any}}","page":"Reference","title":"StartUpDG.MeshData","text":"MeshData(VXYZ, EToV, rd::RefElemData)\nMeshData((VXYZ, EToV), rd::RefElemData)\n\nReturns a MeshData struct with high order DG mesh information from the unstructured mesh information (VXYZ..., EToV).\n\nMeshData(rd::RefElemData, md::MeshData, xyz...)\n\nGiven new nodal positions xyz... (e.g., from mesh curving), recomputes geometric terms and outputs a new MeshData struct. Only fields modified are the coordinate-dependent terms xyz, xyzf, xyzq, rstxyzJ, J, nxyzJ, Jf.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.MeshImportOptions","page":"Reference","title":"StartUpDG.MeshImportOptions","text":"MeshImportOptions\n\nThis struct allows the user to opt for supported features when importing a Gmsh 4.1 .msh file.\n\nSupport\n\ngrouping::Bool | On import would you like to include physical group assignements of 2D elements?\nremap_group_name::Bool | On import would you like to maintain or remap physical group ID? Remap results in groupIds in the range 1:number_group_ids.\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MeshPlotter","page":"Reference","title":"StartUpDG.MeshPlotter","text":"MeshPlotter(rd::RefElemData, md::RefElemData)\n\nPlot recipe to plot a (possibly curved) quadrilateral or triangular mesh. Usage: plot(MeshPlotter(...))\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MultidimensionalQuadrature","page":"Reference","title":"StartUpDG.MultidimensionalQuadrature","text":"MultidimensionalQuadrature\n\nA type parameter for Polynomial indicating that the quadrature has no specific structure. Example usage: \n\n# these are both equivalent\napproximation_type = Polynomial{MultidimensionalQuadrature}() \napproximation_type = Polynomial(MultidimensionalQuadrature())\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.MultipleRefElemData","page":"Reference","title":"StartUpDG.MultipleRefElemData","text":"struct MultipleRefElemData{T <: NamedTuple}\n data::T\nend\n\nHolds multiple RefElemData objects in data where typeof(data) <: NamedTuple.\n\nIndividual RefElemData can be accessed via getproperty, for example rds.Tri. \n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.NamedArrayPartition","page":"Reference","title":"StartUpDG.NamedArrayPartition","text":"NamedArrayPartition(; kwargs...)\nNamedArrayPartition(x::NamedTuple)\n\nSimilar to an ArrayPartition but the individual arrays can be accessed via the constructor-specified names. However, unlike ArrayPartition, each individual array must have the same element type. \n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.NonConformingMesh","page":"Reference","title":"StartUpDG.NonConformingMesh","text":"warning: Experimental implementation\nThis is an experimental feature and may change without warning in future releases.\n\nThis is a proof of concept implementation of a non-conforming mesh in StartUpDG.jl. The intended usage is as follows:\n\nrd = RefElemData(Quad(), N=7)\nmd = MeshData(NonConformingQuadMeshExample(), rd)\n\n(; x, y) = md\nu = @. sin(pi * x) * sin(pi * y)\n\n# interpolate to faces\nnum_total_faces = num_faces(rd.element_type) * md.num_elements\nuf = reshape(rd.Vf * u, :, num_total_faces)\n\n# interpolate faces to mortars (`uf` denotes mortar faces for `NonConformingMesh` types)\n(; nonconforming_faces, mortar_interpolation_matrix) = md.mesh_type\n\nu_mortar = reshape(mortar_interpolation_matrix * uf[:, nonconforming_faces], :, 2 * length(nonconforming_faces))\n\n# construct interior (uM = u⁻ \"minus\") values and exterior (uP = u⁺ \"plus\") values\nuM = hcat(uf, u_mortar) # uM = both element faces and mortar faces\nuP = uM[md.mapP]\n\nThe mortar_projection_matrix similarly maps values from 2 mortar faces back to values on the original non-conforming face. These can be used to create DG solvers on non-conforming meshes.\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.PhysicalFrame","page":"Reference","title":"StartUpDG.PhysicalFrame","text":"`PhysicalFrame{NDIMS} <: AbstractElemShape{NDIMS}`\n\nPhysicalFrame element type. Uses a total degree N approximation space, but is computed with a tensor product Legendre basis as opposed to a triangular PKDO basis. Stores fields shifting and scaling to shift/scale physical coordinates so that they are on the reference element. \n\nPhysicalFrame()\nPhysicalFrame(x, y)\nPhysicalFrame(x, y, vx, vy): stores coordinates `vx, vy` of background Cartesian cell\n\nConstructors for a PhysicalFrame object (optionally uses arrays of points x, y on a cut element).\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.Polynomial","page":"Reference","title":"StartUpDG.Polynomial","text":"Polynomial{T}\n\nRepresents polynomial approximation types (as opposed to finite differences). By default, Polynomial() constructs a Polynomial{StartUpDG.DefaultPolynomialType}. Specifying a type parameters allows for dispatch on additional structure within a polynomial approximation (e.g., collocation, tensor product quadrature, etc). \n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.RefElemData","page":"Reference","title":"StartUpDG.RefElemData","text":"struct RefElemData\n\nRefElemData: contains info (interpolation points, volume/face quadrature, operators) for a high order nodal basis on a given reference element. \n\nExample:\n\nN = 3\nrd = RefElemData(Tri(), N)\n(; r, s ) = rd\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem; N, kwargs...)\nRefElemData(elem, approx_type; N, kwargs...)\n\nKeyword argument constructor for RefElemData (to \"label\" N via rd = RefElemData(Line(), N=3))\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Line, Polynomial{MultidimensionalQuadrature}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem::Line, approximation_type, N;\n quad_rule_vol = quad_nodes(elem, N+1))\nRefElemData(elem, approximation_type, N;\n quad_rule_vol = quad_nodes(elem, N),\n quad_rule_face = quad_nodes(face_type(elem), N))\n\nConstructor for RefElemData for different element types.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Line, SBP{TensorProductLobatto}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elementType::Line, approxType::SBP, N)\nRefElemData(elementType::Quad, approxType::SBP, N)\nRefElemData(elementType::Hex, approxType::SBP, N)\nRefElemData(elementType::Tri, approxType::SBP, N)\n\nSBP reference element data for Quad(), Hex(), and Tri() elements. \n\nFor Line(), Quad(), and Hex(), approxType is SBP{TensorProductLobatto}.\n\nFor Tri(), approxType can be SBP{Kubatko{LobattoFaceNodes}}, SBP{Kubatko{LegendreFaceNodes}}, or SBP{Hicken}. \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Pyr, Polynomial{MultidimensionalQuadrature}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem::Pyr, \n approximation_type::Polynomial, N;\n quad_rule_vol=quad_nodes(elem, N),\n quad_rule_face_quad=quad_nodes(Quad(), N), \n quad_rule_face_tri=quad_nodes(Tri(), N), \n quad_rule_face=(quad_rule_face_quad, quad_rule_face_tri),\n Nplot=10)\n\nBuilds operators for pyramids.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Union{Hex, Line, Quad}, Polynomial{<:TensorProductGaussCollocation}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem::Union{Line, Quad, Hex}, approximation_type::Polynomial{Gauss}, N)\n\nBuilds a rd::RefElemData with (N+1)-point Gauss quadrature in each dimension. \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Union{Tet, Tri, Pyr}, Polynomial{<:TensorProductQuadrature}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem::Union{Tri, Tet, Pyr}, approx_type::Polynomial{<:TensorProductQuadrature}, N; kwargs...)\nRefElemData(elem::Union{Wedge}, \n approx_type::Polynomial{<:TensorProductQuadrature}, N; \n quad_rule_tri = stroud_quad_nodes(Tri(), 2 * N),\n quad_rule_line = gauss_quad(0, 0, N),\n kwargs...)\n\nUses collapsed coordinate volume quadrature. Should be called via\n\nRefElemData(Tri(), Polynomial(TensorProductQuadrature()), N)\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.RefElemData-Tuple{Wedge, Polynomial{MultidimensionalQuadrature}, Any}","page":"Reference","title":"StartUpDG.RefElemData","text":"RefElemData(elem::Wedge, approximation_type::Polynomial, N;\n quad_rule_vol=quad_nodes(elem, N),\n quad_rule_face_quad=quad_nodes(Quad(), N), \n quad_rule_face_tri=quad_nodes(Tri(), N), \n quad_rule_face=(quad_rule_face_quad, quad_rule_face_tri),\n Nplot=10)\n\nBuilds operators for prisms/wedges\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.TensorProductGaussCollocation","page":"Reference","title":"StartUpDG.TensorProductGaussCollocation","text":"TensorProductGaussCollocation\n\nPolynomial{TensorProductGaussCollocation} type indicates a tensor product \n\n(N+1)-point Gauss quadrature on tensor product elements.\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.TensorProductQuadrature","page":"Reference","title":"StartUpDG.TensorProductQuadrature","text":"TensorProductQuadrature{T}\n\nA type parameter to Polynomial indicating that the quadrature has a tensor product structure. Example usage: \n\n# these are both equivalent\napproximation_type = Polynomial{TensorProductQuadrature}(gauss_quad(0, 0, 1)) \napproximation_type = Polynomial(TensorProductQuadrature(gauss_quad(0, 0, 1)))\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.VertexMappedMesh","page":"Reference","title":"StartUpDG.VertexMappedMesh","text":"struct VertexMappedMesh\n\nThe default MeshData mesh type, represents a mesh which is defined purely by vertex locations and element-to-vertex connectivities. For example, these include affine triangular meshes or bilinear quadrilateral or trilinear hexahedral meshes.\n\nFields\n\nelement_type :: TE <: AbstractElemShape \nVXYZ :: TV \nEToV :: TEV\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#StartUpDG.VertexMeshPlotter","page":"Reference","title":"StartUpDG.VertexMeshPlotter","text":"VertexMeshPlotter((VX, VY), EToV, fv)\nVertexMeshPlotter(triout::TriangulateIO)\n\nPlot recipe to plot a quadrilateral or triangular mesh. Usage: plot(VertexMeshPlotter(...))\n\n\n\n\n\n","category":"type"},{"location":"index_refs/#NodesAndModes.equi_nodes-Tuple{PhysicalFrame{2, Shifting, Scaling} where {Shifting<:(StaticArraysCore.SVector{2}), Scaling<:(StaticArraysCore.SVector{2})}, Any, Any}","page":"Reference","title":"NodesAndModes.equi_nodes","text":"function NodesAndModes.equi_nodes(elem::PhysicalFrame, curve, N)\n\nReturns back Np(N) equally spaced nodes on the background quadrilateral corresponding to elem, with points inside of curve removed.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.MeshData_to_vtk","page":"Reference","title":"StartUpDG.MeshData_to_vtk","text":"MeshDatatovtk(md, rd, dim, data, dataname, datatype, filename, writedata = false, equidist_nodes = true)\n\nTranslate the given mesh into a vtk-file. md holds a MeshData object rd holds a reference element data/RefElemData of a TensorProductWedge data holds an array of arrays (of size num_nodes by num_elements) with plotting data dataname is an array of strings with name of the associated data write_data, flag if data should be written or not (e.g., if data is not written, only the mesh will be saved as output) equi_dist_nodes flag if points should be interpolated to equidstant nodes\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.MeshData_to_vtk-Union{Tuple{DIM}, Tuple{MeshData, RefElemData{DIM, ElemShape} where ElemShape<:AbstractElemShape{DIM}, Any, Any, Any}, Tuple{MeshData, RefElemData{DIM, ElemShape} where ElemShape<:AbstractElemShape{DIM}, Vararg{Any, 4}}, Tuple{MeshData, RefElemData{DIM, ElemShape} where ElemShape<:AbstractElemShape{DIM}, Vararg{Any, 5}}} where DIM","page":"Reference","title":"StartUpDG.MeshData_to_vtk","text":"MeshData_to_vtk(md, rd, dim, data, dataname, datatype, filename, write_data = false, equi_dist_nodes = true)\n\nTranslate the given mesh into a vtk-file. md holds a MeshData object rd holds a reference element data/RefElemData object. data holds an array of arrays (of size num_nodes by num_elements) with plotting data dataname is an array of strings with name of the associated data write_data, flag if data should be written or not (e.g., if data is not written, only the mesh will be saved as output) equi_dist_nodes flag if points should be interpolated to equidstant nodes\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.SUD_to_vtk_order-Union{Tuple{RefElemData{DIM, ElemShape} where ElemShape<:AbstractElemShape{DIM}}, Tuple{DIM}} where DIM","page":"Reference","title":"StartUpDG.SUD_to_vtk_order","text":"SUD_to_vtk_order(rd::RefElemData, dim)\n\nCompute the permutation of the nodes between StartUpDG and VTK\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.boundary_face_centroids-Tuple{Any}","page":"Reference","title":"StartUpDG.boundary_face_centroids","text":"function boundary_face_centroids(md)\n\nReturns face centroids and boundary_face_ids on the boundaries of the domain given by md::MeshData.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.build_node_maps-Tuple{Any, Any}","page":"Reference","title":"StartUpDG.build_node_maps","text":"build_node_maps(FToF, Xf)\n\nIntialize the connectivity table along all edges and boundary node tables of all elements. mapM - map minus (interior). mapP - map plus (exterior).\n\nXf = (xf, yf, zf) and FToF is size (Nfaces * K) and FToF[face] = face neighbor\n\nmapM, mapP are size Nfp x (Nfaces*K)\n\nExamples\n\njulia> mapM, mapP, mapB = build_node_maps(FToF, (xf, yf))\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.caratheodory_pruning_qr-Tuple{Any, Any}","page":"Reference","title":"StartUpDG.caratheodory_pruning_qr","text":"caratheodory_pruning_qr(V, w_in)\n\nThis performs Caratheodory pruning using a naive QR-based algorithm. Returns (w, inds), where inds denotes sub-selected indices for a reduced quadrature rule, and w is a vector of reduced positive weights.\n\nThe original Matlab code this was based on was authored by Akil Narayan.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.ck45-Tuple{}","page":"Reference","title":"StartUpDG.ck45","text":"ck45()\n\nReturns coefficients rka,rkb,rkc for the 4th order 5-stage low storage Carpenter/Kennedy Runge Kutta method. Coefficients evolve the residual, solution, and local time, e.g.,\n\nExample\n\nfor i in eachindex(rk4a, rk4b)\n @. res = rk4a[i] * res + dt * rhs # i = RK stage\n @. u += rk4b[i] * res\nend\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.connect_mesh-Tuple{Any, Any}","page":"Reference","title":"StartUpDG.connect_mesh","text":"connect_mesh(EToV,fv)\n\nInputs:\n\nEToV is a num_elements by Nv matrix whose rows identify the Nv vertices\n\nwhich make up one of the num_elements elements.\n\nfv (an array of arrays containing unordered indices of face vertices).\n\nOutput: FToF, an length(fv) by num_elements index array containing face-to-face connectivity.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.connect_mesh-Tuple{RefElemData, Any, Any}","page":"Reference","title":"StartUpDG.connect_mesh","text":"connect_mesh(rd, face_centroids, region_flags, cutcells; tol = 1e2 * eps())\n\nConnects faces of a cut mesh to each other, returns FToF such that face f is connected to FToF[f]. \n\nInputs:\n\nrd::RefElemData\nfacecentroids = (facecentroidsx, facecentroidsy), where `facecentroids_x/y` are vectors of coordinates of face centroids\nregion_flags, cutcells are return arguments from PathIntersections.define_regions\n\nThe keyword argument tol is the tolerance for matches between face centroids. \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.construct_cut_surface_quadrature","page":"Reference","title":"StartUpDG.construct_cut_surface_quadrature","text":"construct_cut_surface_quadrature(N, cutcells, quad_rule_1D = gauss_quad(0, 0, N))\n\nConstructs cut surface quadrature using a degree N geometric mapping and a reference quadrature rule quad_rule_1D. Returns xf, yf, nxJ, nyJ, wf which are vectors, and face_node_indices, which is a Vector{Vector{Int}} of global face node indices (which index into xf.cut, yf.cut, etc) for each face of each cut element.\n\nOn boundaries of cut cells, the surface quadrature is taken to be exact for degree N^2 + (N-1) polynomials. This ensures satisfaction of a weak GSBP property.\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.construct_cut_volume_quadrature-Tuple{Any, Any, Any}","page":"Reference","title":"StartUpDG.construct_cut_volume_quadrature","text":"construct_cut_volume_quadrature(N, cutcells; target_degree = 2 * N - 1)\n\nConstructs volume quadrature using subtriangulations of cut cells and Caratheodory pruning. The resulting quadrature is exact for polynomials of degree target_degree. \n\nWe set target_degree to 2 * N - 1 by default, which is sufficient to ensure that ∫du/dx * v is integrated exactly so that integration by parts holds under the generated cut cell quadrature. \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.construct_physical_frame_elements-NTuple{4, Any}","page":"Reference","title":"StartUpDG.construct_physical_frame_elements","text":"construct_physical_frame_elements(region_flags, cutcells)\n\nComputes physical frame shifting and scaling parameters from the vertices of cut cells and the background cell location.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.estimate_h-Union{Tuple{DIM}, Tuple{RefElemData{DIM, ElemShape} where ElemShape<:AbstractElemShape{DIM}, MeshData{DIM}}} where DIM","page":"Reference","title":"StartUpDG.estimate_h","text":"estimate_h(rd::RefElemData, md::MeshData)\nestimate_h(e, rd::RefElemData, md::MeshData) # e = element index\n\nEstimates the mesh size via min sizeofdomain * |J|/|Jf|, since |J| = O(hᵈ) and |Jf| = O(hᵈ⁻¹). \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.findline-Tuple{String, Vector{String}}","page":"Reference","title":"StartUpDG.findline","text":"findline(word::String, lines)\n\nOutputs the line number of word in lines. \n\nIt is assumed that the word exists at least once in the file.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.get_boundary_face_labels-Tuple{Triangulate.TriangulateIO, RefElemData{2, Tri}, MeshData{2}}","page":"Reference","title":"StartUpDG.get_boundary_face_labels","text":"function get_boundary_face_labels(triout::TriangulateIO, md::MeshData{2})\n\nFind Triangle segment labels of boundary faces. Returns two arguments:\n\nboundary_face_tags: tags of faces on the boundary\nboundary_faces: list of faces on the boundary of the domain\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.get_node_boundary_tags-Tuple{Triangulate.TriangulateIO, RefElemData{2, Tri}, MeshData{2}}","page":"Reference","title":"StartUpDG.get_node_boundary_tags","text":"function get_node_boundary_tags(triout::TriangulateIO,md::MeshData{2},rd::RefElemData{2,Tri})\n\nComputes node_tags = Nfp x Nfaces * num_elements array where each entry is a Triangulate.jl tag number.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.get_num_elements","page":"Reference","title":"StartUpDG.get_num_elements","text":"returns the number of elements in a .msh file of a specified dimension\n\nNotes: Gmsh includes elements in a .msh file of multiple dimensions. We want a count of how many\n\n2D elements are in our file. This corisponds to the number of elements in our tri mesh.\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.hex_vtk_order","page":"Reference","title":"StartUpDG.hex_vtk_order","text":"hex_vtk_order(corner_verts, order, dim, skip = false)\n\nCompute the coordinates of a VTKLAGRANGEHEXAHEDRON of a hex of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_HEXHEDRON\n\nInspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py\n\nVTK node numbering of a hexagon:\n\n 8+------+7\n /| /|\n / | / |\n 5+------+6 |\n\nz | 4+–-|–+3 | y | / | / |/ |/ |/ 0–> x 1+–––+2\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.hybridized_SBP_operators-Tuple{Any}","page":"Reference","title":"StartUpDG.hybridized_SBP_operators","text":"function hybridized_SBP_operators(rd::RefElemData{DIMS})\n\nConstructs hybridized SBP operators given a RefElemData. Returns operators Qrsth..., VhP, Ph.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.hybridized_SBP_operators-Tuple{MeshData{2, <:StartUpDG.CutCellMesh}}","page":"Reference","title":"StartUpDG.hybridized_SBP_operators","text":"hybridized_SBP_operators(md::MeshData{2, <:CutCellMesh})\n\nThis constructs hybridized SBP operators using the approach taken in Chan (2019), \"Skew-Symmetric Entropy Stable Modal Discontinuous Galerkin Formulations\". https://doi.org/10.1007/s10915-019-01026-w\n\nThis function returns hybridized_operators::Vector{Tuple{<:Matrix, <:Matrix}} and project_and_interp_operators, projection_operators, interpolation_operators, which are all Vector{<:Matrix}, where each entry corresponds to a cut element.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.inverse_trace_constant-Tuple{RefElemData{1, Line, <:Polynomial}}","page":"Reference","title":"StartUpDG.inverse_trace_constant","text":"function inverse_trace_constant(rd::RefElemData)\n\nReturns the degree-dependent constant in the inverse trace equality over the reference element (as reported in \"GPU-accelerated dG methods on hybrid meshes\" by Chan, Wang, Modave, Remacle, Warburton 2016).\n\nCan be used to estimate dependence of maximum stable timestep on degree of approximation.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.make_periodic-Union{Tuple{MeshData{Dim}}, Tuple{Dim}, Tuple{MeshData{Dim}, Bool}} where Dim","page":"Reference","title":"StartUpDG.make_periodic","text":"make_periodic(md::MeshData{Dim}, is_periodic...) where {Dim}\nmake_periodic(md::MeshData{Dim}, is_periodic = ntuple(x -> true, Dim)) where {Dim}\nmake_periodic(md::MeshData, is_periodic = true)\n\nReturns new MeshData such that the node maps mapP and face maps FToF are now periodic. Here, is_periodic is a tuple of Bool indicating whether or not to impose periodic BCs in the x,y, or z coordinate.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.n_verts_between-Tuple{Any, Any, Any}","page":"Reference","title":"StartUpDG.n_verts_between","text":"n_verts_between(n, from, to, dim)\n\nCompute the coordinates of n equally distributed points between the points given by from and to. dim is the dimension of from and to. Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.quad_vtk_order","page":"Reference","title":"StartUpDG.quad_vtk_order","text":"quad_vtk_order(corner_verts, order, dim, skip = false)\n\nCompute the coordinates of a VTKLAGRANGEQUAD of a quad of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_QUAD Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.read_Gmsh_2D-Tuple{String, Vararg{Any}}","page":"Reference","title":"StartUpDG.read_Gmsh_2D","text":"read_Gmsh_2D(filename, args...)\n\nReads a 2D triangular Gmsh file. Mesh formats 2.2 and 4.1 supported. Returns (VX, VY), EToV. \n\nExamples\n\nVXY, EToV = read_Gmsh_2D(\"eulerSquareCylinder2D.msh\") # v2.2 file format\nVXY, EToV = read_Gmsh_2D(\"test/testset_Gmsh_meshes/periodicity_mesh_v4.msh\") # v4.1 file format\n\n# if MeshImportOptions.grouping=true, then a third variable `grouping` is returned\nVXY, EToV, grouping = read_Gmsh_2D(\"test/testset_Gmsh_meshes/periodicity_mesh_v4.msh\", MeshImportOptions(true, false))\nVXY, EToV, grouping = read_Gmsh_2D(\"test/testset_Gmsh_meshes/periodicity_mesh_v4.msh\", true) # same as above\n\nSee also\n\nhttps://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format\nhttps://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format-version-2-0028Legacy0029\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.read_Gmsh_2D_v2-Tuple{String}","page":"Reference","title":"StartUpDG.read_Gmsh_2D_v2","text":"read_Gmsh_2D_v2(filename)\n\nReads triangular GMSH 2D file format 2.2 0 8. Returns (VX, VY), EToV.\n\nExamples\n\nVXY, EToV = read_Gmsh_2D_v2(\"eulerSquareCylinder2D.msh\")\n\nhttps://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format-version-2-0028Legacy0029\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.read_Gmsh_2D_v4","page":"Reference","title":"StartUpDG.read_Gmsh_2D_v4","text":"For brevity when grouping is the only supported feature.\n\nexample: VXY, EToV, grouping = read_Gmsh_2D_v4(\"file.msh\",true)\nexample: VXY, EToV = read_Gmsh_2D_v4(\"file.msh\",false)\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.read_Gmsh_2D_v4-Tuple{String, MeshImportOptions}","page":"Reference","title":"StartUpDG.read_Gmsh_2D_v4","text":"function read_Gmsh_2D_v4(filename, options)\n\nreads triangular GMSH 2D .msh files.\n\nOutput\n\nThis depends on if grouping is opted for or not\n\nreturns: (VX, VY), EToV\nreturns: (VX, VY), EToV, grouping\n\nSupported formats and features:\n\nversion 4.1 'physical group support 'remap group ids\n\ngrouping application\n\nWhen modeling the wave equation you might want wave speeds to vary across your domain. By assigning physical groups in Gmsh we can maintain such groupings upon importing the .msh file. Each imported element will be a member of a phyical group.\n\nVXY, EToV = read_Gmsh_2D_v4(\"eulerSquareCylinder2D.msh\")\nVXY, EToV = read_Gmsh_2D_v4(\"eulerSquareCylinder2D.msh\",false)\nVXY, EToV, grouping = read_Gmsh_2D_v4(\"eulerSquareCylinder2D.msh\", true)\n\noption = MeshImportOption(true)\nVXY, EToV, grouping = read_Gmsh_2D_v4(\"eulerSquareCylinder2D.msh\", option)\n\nhttps://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format\n\nNotes: the version 4 format has a more detailed block data format this leads to more complicated parser.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.refine","page":"Reference","title":"StartUpDG.refine","text":"function refine(triout, h, href = h/2)\n\nRefinement of a previous mesh given the current mesh size h. Preserves boundary/volume tags.\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.remap_element_grouping-Tuple{Vector{Int64}}","page":"Reference","title":"StartUpDG.remap_element_grouping","text":"remapelementgrouping!(eg::Vector{Int}) GMSH uses integers for naming conventions. This function remaps the Gmsh ids to a list of ids 1:numGroups. This just cleans up a little after Gmsh\n\nExample output\n\nremapelementgrouping([16,16,17,17]) -> [1,1,2,2]\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.sort_by_axis-Tuple{Any}","page":"Reference","title":"StartUpDG.sort_by_axis","text":"sort_by_axis(corner_verts)\n\nGiven the points 'corner_verts' sort them in a lexicographical order and return the permutated points. \n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.sparse_low_order_SBP_operators-Union{Tuple{RefElemData{NDIMS, ElemShape} where ElemShape<:AbstractElemShape{NDIMS}}, Tuple{NDIMS}} where NDIMS","page":"Reference","title":"StartUpDG.sparse_low_order_SBP_operators","text":"function sparse_low_order_SBP_operators(rd; factor=1.01)\n\nConstructs sparse low order SBP operators given a RefElemData. Returns operators Qrst..., E ≈ Vf * Pq that satisfy a generalized summation-by-parts (GSBP) property:\n\n `Q_i + Q_i^T = E' * B_i * E`\n\nfactor is a scaling which determines how close a node must be to another node to be considered a neighbor.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.subcell_limiting_operators-Tuple{RefElemData}","page":"Reference","title":"StartUpDG.subcell_limiting_operators","text":"Δrst, Rrst = subcell_limiting_operators(rd::RefElemData)\n\nReturns tuples of subcell limiting operators Drst = (Δr, Δs, ...) and R = (Rr, Rs, ...) such that for r where sum(r) = 0, sum(D * Diagonal(θ) * R * r) = 0 for any choice of θ. These operators are useful for conservative subcell limiting techniques (see https://doi.org/10.1016/j.compfluid.2022.105627 for an example of such an approach on tensor product elements). \n\nSparse SBP operators used in an intermediate step when buidling these subcell limiting operators; by default, these operators are constructed using sparse_low_order_SBP_operators. To construct subcell limiting operators for a general SBP operator, one can use the following:\n\nΔ, R = subcell_limiting_operators(Q::AbstractMatrix; tol = 100 * eps())\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.subtriangulated_cutcell_quadrature","page":"Reference","title":"StartUpDG.subtriangulated_cutcell_quadrature","text":"subtriangulated_cutcell_quadrature(cutcell, rd_tri::RefElemData, \n r1D = gauss_lobatto_quad(0,0,rd_tri.N))\n\nConstructs a quadrature from subtriangulations. The degree of both the quadrature rule and isoparametric mapping are specified by rd_tri. \n\nThe optional argument r1D specifies the nodal points used for constructing a curved mapping via interpolatory warp and blend. \n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.tag_boundary_faces-Tuple{Any, Nothing}","page":"Reference","title":"StartUpDG.tag_boundary_faces","text":"function tag_boundary_faces(md, boundary_name::Symbol = :entire_boundary)\nfunction tag_boundary_faces(md, boundary_list::Dict{Symbol, <:Function})\n\nWhen called without arguments, just returns Dict(:entire_boundary => boundary_faces)`.\n\nExample usage: \n\njulia> rd = RefElemData(Tri(), N=1)\njulia> md = MeshData(uniform_mesh(Tri(), 2)..., rd)\njulia> on_bottom_boundary(x, y, tol = 1e-13) = abs(y+1) < tol\njulia> on_top_boundary(x, y, tol = 1e-13) = abs(y-1) < tol\njulia> tag_boundary_faces(Dict(:bottom => on_bottom_boundary,\n :top => on_top_boundary), md)\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.tag_boundary_faces-Tuple{Triangulate.TriangulateIO, RefElemData{2, Tri}, MeshData{2}, NamedTuple}","page":"Reference","title":"StartUpDG.tag_boundary_faces","text":"function tag_boundary_faces(triout::TriangulateIO,\n rd::RefElemData{2,Tri}, md::MeshData{2},\n boundary_list::Union{NamedTuple,Dict{Symbol,Int}})\n\nHere, boundary_list is a Dict (or NamedTuple) whose values are the boundary tags for a TriangulateIO mesh format. The output is a Dict or NamedTuple with keys given by boundary_list and values equal to vectors of faces on that given boundary.\n\nExample usage:\n\njulia> using Triangulate, StartUpDG\njulia> triout = scramjet()\njulia> rd = RefElemData(Tri(),N=1)\njulia> md = MeshData(triangulateIO_to_VXYEToV(triout)...,rd)\njulia> tag_boundary_faces(triout,rd,md, Dict(:wall=>1, :inflow=>2, :outflow=>3))\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.triangle_vtk_order","page":"Reference","title":"StartUpDG.triangle_vtk_order","text":"triangle_vtk_order(corner_verts, order, dim, skip = false)\n\nCompute the coordinates of a VTK_LAGRANGE_TRIANGLE of a triangle or order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. If skip is set to true, the coordinates of the vertex- and edge-points aren't computed, which can be used to compute points of a VTK_LAGRANGE_TRIANGLE Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py\n\n\n\n\n\n","category":"function"},{"location":"index_refs/#StartUpDG.triangulateIO_to_VXYEToV-Tuple{Triangulate.TriangulateIO}","page":"Reference","title":"StartUpDG.triangulateIO_to_VXYEToV","text":"function triangulateIO_to_VXYEToV(triout::TriangulateIO)\n\nComputes VX,VY,EToV from a TriangulateIO object.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.type_to_vtk-Tuple{Hex}","page":"Reference","title":"StartUpDG.type_to_vtk","text":"type_to_vtk(elem::Hex)\nreturn the VTK-type\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.type_to_vtk-Tuple{Quad}","page":"Reference","title":"StartUpDG.type_to_vtk","text":"type_to_vtk(elem::Quad)\nreturn the VTK-type\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.type_to_vtk-Tuple{Tri}","page":"Reference","title":"StartUpDG.type_to_vtk","text":"type_to_vtk(elem::Tri)\nreturn the VTK-type\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.type_to_vtk-Tuple{Wedge}","page":"Reference","title":"StartUpDG.type_to_vtk","text":"type_to_vtk(elem::Wedge)\nreturn the VTK-type\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.uniform_mesh-Tuple{Line, Any}","page":"Reference","title":"StartUpDG.uniform_mesh","text":"uniform_mesh(elem::Line,Kx)\nuniform_mesh(elem::Tri,Kx,Ky)\nuniform_mesh(elem::Quad,Kx,Ky)\nuniform_mesh(elem::Hex,Kx,Ky,Kz)\nuniform_mesh(elem, K)\n\nUniform Kx (by Ky by Kz) mesh on -11^d, where d is the spatial dimension. Returns (VX,VY,VZ), EToV. When only one K is specified, it assumes a uniform mesh with K elements in each coordinate direction.\n\nK can also be specified using a keyword argument K1D, e.g., uniform_mesh(elem; K1D = 16).\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.vtk_order-Tuple{Hex, Any}","page":"Reference","title":"StartUpDG.vtk_order","text":"vtk_order(elem::Hex, order)\n\nConstruct all node-points of a VTKLAGRANGEHEXAHEDRON of order order. The corner-nodes are given by the reference hexahedron used by StartUpDG in the order defined by vtk.\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.vtk_order-Tuple{Quad, Any}","page":"Reference","title":"StartUpDG.vtk_order","text":"vtk_order(elem::Quad, order)\n\nConstruct all node-points of a VTKLAGRANGEQUAD of order order. The corner-nodes are given by the reference quadrilateral used by StartUpDG in the order defined by vtk\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.vtk_order-Tuple{Tri, Any}","page":"Reference","title":"StartUpDG.vtk_order","text":"vtk_order(elem::Tri, order)\n\nConstruct all node-points of a VTK_LAGRANGE_TRIANGLE of order order. The corner-nodes are given by the reference-triangle used by StartUpDG in the order defined by vtk\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.vtk_order-Tuple{Wedge, Any}","page":"Reference","title":"StartUpDG.vtk_order","text":"vtk_order(elem::Wedge, order)\n\nConstruct all node-points of a VTKLAGRANGEWEDGE of order order. The corner-nodes are given by the reference-wedge used by StartUpDG\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#StartUpDG.wedge_vtk_order-Tuple{Any, Any, Any}","page":"Reference","title":"StartUpDG.wedge_vtk_order","text":"wedge_vtk_order(corner_verts, order, dim)\n\nCompute the coordinates of a VTKLAGRANGEWEDGE of order order defined by the coordinates of the vertices given in corner_verts. dim is the dimension of the coordinates given. Inspired by: https://github.com/ju-kreber/paraview-scripts/blob/master/node_ordering.py\n\n\n\n\n\n","category":"method"},{"location":"index_refs/#Triangulate.triangulate","page":"Reference","title":"Triangulate.triangulate","text":"function Triangulate.triangulate(triin::TriangulateIO, maxarea, minangle=20)\n\nConvenience routine to avoid writing out @sprintf each time. Returns a TriangulateIO object.\n\n\n\n\n\n","category":"function"},{"location":"tstep_usage/#Time-stepping","page":"Timestepping","title":"Time-stepping","text":"","category":"section"},{"location":"tstep_usage/","page":"Timestepping","title":"Timestepping","text":"For convenience, we include a commonly used explicit Runge-Kutta scheme. For more advanced time-stepping functionality, we recommend OrdinaryDiffEq.jl. ","category":"page"},{"location":"tstep_usage/#Carpenter-and-Kennedy's-(4,5)-method","page":"Timestepping","title":"Carpenter and Kennedy's (4,5) method","text":"","category":"section"},{"location":"tstep_usage/","page":"Timestepping","title":"Timestepping","text":"ck45() returns coefficients for a low-storage Runge-Kutta method.","category":"page"},{"location":"tstep_usage/#Example-usage:","page":"Timestepping","title":"Example usage:","text":"","category":"section"},{"location":"tstep_usage/","page":"Timestepping","title":"Timestepping","text":"using Plots\nusing StartUpDG\n\n# Brusselator\nB = 3\nf(y1, y2) = [1 + y1^2 * y2 - (B+1) * y1, B * y1 - y1^2 * y2]\nf(Q) = f(Q[1], Q[2])\np,q = 1.5, 3.0\nQ = [p; q]\n\ndt = .1\nFinalTime = 20\n\nres = zero.(Q) # init RK residual\nrk4a, rk4b, rk4c = ck45()\nNsteps = ceil(FinalTime / dt)\ndt = FinalTime / Nsteps\n\nplot() # init plot\nfor i = 1:Nsteps\n global res # yes, I know...this is just for simplicty\n for INTRK = 1:5\n rhsQ = f(Q)\n @. res = rk4a[INTRK] * res + dt * rhsQ # i = RK stage\n @. Q = Q + rk4b[INTRK] * res\n end\n scatter!([i*dt;i*dt],Q)\nend\ndisplay(plot!(leg=false))","category":"page"},{"location":"more_meshes/#Additional-mesh-types","page":"Additional mesh types","title":"Additional mesh types","text":"","category":"section"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"In addition to more \"standard\" mesh types, StartUpDG.jl also has experimental support for hybrid and cut-cell meshes. Both are currently restricted to two dimensional domains.","category":"page"},{"location":"more_meshes/#Hybrid-meshes","page":"Additional mesh types","title":"Hybrid meshes","text":"","category":"section"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"warning: Experimental implementation\nThis is an experimental feature and may change in future releases.","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"There is initial support for hybrid meshes in StartUpDG.jl. The following is a short example where we interpolate a polynomial and compute its derivative.","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"rds = RefElemData((Tri(), Quad()), N = 3)\n\n# Simple hybrid mesh for testing\n# 1 7______8______9\n# | | 3 / |\n# | 4 | / 5 |\n# 0 4 ---- 5 ---- 6 \n# | | |\n# | 1 | 2 |\n# -1 1 ---- 2 ---- 3\n# -1 0 1\nVX = [-1; 0; 1; -1; 0; 1; -1; 0; 1]\nVY = [-1; -1; -1; 0; 0; 0; 1; 1; 1]\nEToV = [[1 2 4 5], [2 3 5 6], [5 8 9], [4 5 7 8], [9 6 5]]\n\nmd = MeshData(VX, VY, EToV, rds)\n\n# test that the local derivatives of a polynomial recover the exact derivative\n(; x, y ) = md\nu = @. x^3 - x^2 * y + 2 * y^3\ndudx = @. 3 * x^2 - 2 * x * y\n\n# compute local derivatives\n(; rxJ, sxJ, J ) = md\ndudr, duds = similar(md.x), similar(md.x)\ndudr.Quad .= rds[Quad()].Dr * u.Quad\nduds.Quad .= rds[Quad()].Ds * u.Quad\ndudr.Tri .= rds[Tri()].Dr * u.Tri\nduds.Tri .= rds[Tri()].Ds * u.Tri\n\n@show norm(@. dudx - (rxJ * dudr + sxJ * duds) / J) # should be O(1e-14)","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"The main difference in the representation of hybrid meshes compared with standard MeshData objects is the use of NamedArrayPartition arrays as storage for the geometric coordinates. These arrays have \"fields\" corresponding to the element type, for example","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"md.x.Tri\nmd.x.Quad","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"but can still be indexed as linear arrays. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"The mapP field behaves similarly. If we interpolate the values of u for each element type to surface quadrature nodes, we can use mapP to linearly index into the array to find neighbors. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"uf = similar(md.xf)\nuf.Quad .= rds.Quad.Vf * u.Quad\nuf.Tri .= rds.Tri.Vf * u.Tri\nuf[md.mapP] # this returns the exterior node values","category":"page"},{"location":"more_meshes/#Cut-Meshes","page":"Additional mesh types","title":"Cut Meshes","text":"","category":"section"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"warning: Experimental implementation\nThis is an experimental feature and may change in future releases.","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"Initial support for cut-cell meshes is available via PathIntersections.jl. By passing in a tuple of curves (defined as parametrized functions of one coordinate, see PathIntersections.jl documentation for more detail), StartUpDG.jl can compute a MeshData for a cut-cell mesh. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"circle = PresetGeometries.Circle(R=0.33, x0=0, y0=0)\ncells_per_dimension_x, cells_per_dimension_y = 4, 4\n\nrd = RefElemData(Quad(), N=3)\nmd = MeshData(rd, (circle, ), cells_per_dimension_x, cells_per_dimension_y, Subtriangulation(); precompute_operators=true)","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"Here, the final argument quadrature_type = Subtriangulation() determines how the quadrature on cut cells is determined. For Subtriangulation(), the quadrature on cut cells is constructed from a curved isoparametric subtriangulation of the cut cell. The number of quadrature points on a cut cell is then reduced (while preserving positivity) using Caratheodory pruning. If not specified, the quadrature_type argument defaults to Subtriangulation(). ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"Quadrature rules can also be constructed by specifying quadrature_type = MomentFitting(). The quadrature points on cut cells md.xq.cut are determined from sampling and a pivoted QR decomposition. This is not recommended, as it can be both slower, and the cut-cell quadrature weights md.wJq.cut are not guaranteed to be positive. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"The interpolation points on cut cells md.x.cut are determined from sampled points and a pivoted QR decomposition. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"The optional keyword argument precompute_operators specifies whether to precompute differentiation, face interpolation, mass, and lifting matrices for each cut cell. If precompute_operators=true, these are stored in md.mesh_type.cut_cell_operators. ","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"As with hybrid meshes, the nodal coordinates md.x, md.y are NamedArrayPartitions with cartesian and cut fields. For example, md.x.cartesian and md.x.cut are the x-coordinates of the Cartesian and cut cells, respectively. Likewise, md.mapP indexes linearly into the array of face coordinates and specifies exterior node indices. For example, we can interpolate a function to face nodes and compute exterior values via the following code:","category":"page"},{"location":"more_meshes/","page":"Additional mesh types","title":"Additional mesh types","text":"(; x, y) = md\nu = @. x^rd.N - x * y^(rd.N-1) - x^(rd.N-1) * y + y^rd.N # some random function \n\n# interpolate the solution to face nodes\nuf = similar(md.xf) \nuf.cartesian .= rd.Vf * u.cartesian\nfor e in 1:size(md.x.cut, 2)\n ids = md.mesh_type.cut_face_nodes[e]\n Vf = md.mesh_type.cut_cell_operators.face_interpolation_matrices[e]\n uf.cut[ids] .= Vf * u.cut[:, e]\nend\n\nuf[md.mapP] # these are \"exterior\" values for each entry of `uf`","category":"page"},{"location":"ex_dg_deriv/#Example:-approximating-derivatives-using-DG","page":"Example: computing DG derivatives","title":"Example: approximating derivatives using DG","text":"","category":"section"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"MeshData can be used to compute DG derivatives. Suppose f is a differentiable function and the domain Omega can be decomposed into non-overlapping elements D^k. The approximation of fracpartial fpartial x can be approximated using the following formulation: find piecewise polynomial u such that for all piecewise polynomials v","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"int_Omega u v = sum_k left( int_D^k fracpartial upartial xv + int_partial D^k frac12 lefturightn_x v right)","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"Here, lefturight = u^+ - u denotes the jump across an element interface, and n_x is the x-component of the outward unit normal on D^k.","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"Discretizing the left-hand side of this formulation yields a mass matrix. Inverting this mass matrix to the right hand side yields the DG derivative. We show how to compute it for a uniform triangular mesh using MeshData and StartUpDG.jl.","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"We first construct the triangular mesh and initialize md::MeshData.","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"using StartUpDG\nusing Plots\n\nN = 3\nK1D = 8\nrd = RefElemData(Tri(), N)\nVXY, EToV = uniform_mesh(Tri(), K1D)\nmd = MeshData(VXY, EToV, rd)","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"We can approximate a function f(x y) using interpolation","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"f(x, y) = exp(-5 * (x^2 + y^2)) * sin(1 + pi*x) * sin(2 + pi*y)\n(; x, y) = md\nu = @. f(x, y)","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"or using quadrature-based projection","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"(; Pq ) = rd\n(; x, y, xq, yq ) = md\nu = Pq * f.(xq, yq)","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"We can use scatter in Plots.jl to quickly visualize the approximation. This is not intended to create a high quality image (see other libraries, e.g., Makie.jl,VTK.jl, or Triplot.jl for publication-quality images).","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"(; Vp ) = rd\nxp, yp, up = Vp * x, Vp * y, Vp * u # interp to plotting points\nscatter(xp, yp, uxp, zcolor=uxp, msw=0, leg=false, ratio=1, cam=(0, 90))","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"Both interpolation and projection create a matrix u of size N_p times K which contains coefficients (nodal values) of the DG polynomial approximation to f(x y). We can approximate the derivative of f(x y) using the DG derivative formulation","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"function dg_deriv_x(u, rd::RefElemData, md::MeshData)\n (; Vf, Dr, Ds, LIFT ) = rd\n (; rxJ, sxJ, J, nxJ, mapP ) = md\n uf = Vf * u\n ujump = uf[mapP] - uf\n\n # derivatives using chain rule + lifted flux terms\n ux = rxJ .* (Dr * u) + sxJ .* (Ds * u) \n dudxJ = ux + LIFT * (.5 * ujump .* nxJ)\n\n return dudxJ ./ J\nend","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"We can visualize the result as follows:","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"dudx = dg_deriv_x(u, rd, md)\nuxp = Vp * dudx\nscatter(xp, yp, uxp, zcolor=uxp, msw=0, leg=false, ratio=1, cam=(0,90))","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"Plots of the polynomial approximation u(xy) and the DG approximation of fracpartial upartial x are given below","category":"page"},{"location":"ex_dg_deriv/","page":"Example: computing DG derivatives","title":"Example: computing DG derivatives","text":"(Image: u) (Image: dudx) ⠀","category":"page"},{"location":"#Overview","page":"Home","title":"Overview","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"This package contains routines to initialize reference element operators, physical mesh arrays, and connectivity arrays for nodal DG methods. The codes roughly based on Nodal Discontinuous Galerkin Methods by Hesthaven and Warburton (2007).","category":"page"},{"location":"#A-short-example","page":"Home","title":"A short example","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"using StartUpDG\n\n# polynomial degree and mesh size\nN = 3\nK1D = 8\n\n# init ref element and mesh\nrd = RefElemData(Tri(), N)\nVXY, EToV = uniform_mesh(Tri(), K1D)\nmd = MeshData(VXY, EToV, rd)\n\n# Define a function by interpolation\n(; x, y ) = md\nu = @. exp(-10 * (x^2 + y^2))\n\n# Compute derivatives using geometric mapping + chain rule\n(; Dr, Ds ) = rd\n(; rxJ, sxJ, J ) = md\ndudx = (rxJ .* (Dr * u) + sxJ .* (Ds * u)) ./ J","category":"page"}] +} diff --git a/v1.1.5/siteinfo.js b/v1.1.5/siteinfo.js new file mode 100644 index 00000000..25ac5e09 --- /dev/null +++ b/v1.1.5/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v1.1.5"; diff --git a/v1.1.5/tstep_usage/index.html b/v1.1.5/tstep_usage/index.html new file mode 100644 index 00000000..d28f5f5e --- /dev/null +++ b/v1.1.5/tstep_usage/index.html @@ -0,0 +1,30 @@ + +Timestepping · StartUpDG.jl

    Time-stepping

    For convenience, we include a commonly used explicit Runge-Kutta scheme. For more advanced time-stepping functionality, we recommend OrdinaryDiffEq.jl.

    Carpenter and Kennedy's (4,5) method

    ck45() returns coefficients for a low-storage Runge-Kutta method.

    Example usage:

    using Plots
+using StartUpDG
+
+# Brusselator
+B = 3
+f(y1, y2) = [1 + y1^2 * y2 - (B+1) * y1, B * y1 - y1^2 * y2]
+f(Q) = f(Q[1], Q[2])
+p,q = 1.5, 3.0
+Q = [p; q]
+
+dt = .1
+FinalTime = 20
+
+res = zero.(Q) # init RK residual
+rk4a, rk4b, rk4c = ck45()
+Nsteps = ceil(FinalTime / dt)
+dt = FinalTime / Nsteps
+
+plot() # init plot
+for i = 1:Nsteps
+    global res # yes, I know...this is just for simplicty
+    for INTRK = 1:5
+        rhsQ = f(Q)
+        @. res = rk4a[INTRK] * res + dt * rhsQ # i = RK stage
+        @. Q =  Q + rk4b[INTRK] * res
+    end
+    scatter!([i*dt;i*dt],Q)
+end
+display(plot!(leg=false))
    diff --git a/versions.js b/versions.js index a84163f8..ea4e961e 100644 --- a/versions.js +++ b/versions.js @@ -19,5 +19,5 @@ var DOC_VERSIONS = [ "v0.3", "dev", ]; -var DOCUMENTER_NEWEST = "v1.1.4"; +var DOCUMENTER_NEWEST = "v1.1.5"; var DOCUMENTER_STABLE = "stable";